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{"sheet":"単振動","index":0,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,7],[3,5,3,7]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"単振動",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,J8:L8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,"マクロは標準モジュール-Module6 の中。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,"解析解",null,null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-($C$25^2)*H8","v":-40.000000000000007},{"$f":"-$C$29*$C$25*SIN($C$25*E8+$C$30)","v":10},{"$f":"$C$29*COS($C$25*E8+$C$30)","v":1},null,-40,10,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-44.680248612306279,9.4916744886538638,1.1170062153076568,null,-44.680247296000005,9.4916746240000016,1.1170061824000002,null,{"$f":"J9-F9","v":1.3163062746457399E-6},{"$f":"K9-G9","v":1.353461378528209E-7},{"$f":"L9-H9","v":-3.2907656599689972E-8}]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-49.103262500841332,8.9287031697966501,1.2275815625210331,null,-49.103260005614651,8.9287034712707332,1.2275815001403663,null,2.4952266812761081E-6,3.0147408303093925E-7,-6.238066685426702E-8]
["質量","m",10,"[kg]",3.6000000000000004E-2,-53.243577332008343,8.3143272020206922,1.3310894333002083,null,-53.243573816795511,8.3143276978010405,1.3310893454198878,null,3.5152128319282383E-6,4.9578034833075435E-7,-8.7880320576161353E-8]
["粘性減衰係数","c",0,"[Ns/m]",4.8000000000000001E-2,-57.077356337324574,7.6520836925998053,1.4269339084331141,null,-57.077351980860939,7.6520844079268056,1.4269337995215234,null,4.3564636342807717E-6,7.1532700030019214E-7,-1.0891159063497469E-7]
["バネ定数","k",400,"[N/m]",0.06,-60.582527547316708,6.945785333528911,1.5145631886829174,null,-60.582522546197133,6.9457862903979501,1.5145630636549283,null,{"$f":"J13-F13","v":5.001119575354096E-6},{"$f":"K13-G13","v":9.5686903911484933E-7},{"$f":"L13-H13","v":-1.2502798907298995E-7}]
["静止摩擦係数","μ",0,"[ND]",7.1999999999999995E-2,-63.738910865052048,6.1994984509574484,1.5934727716263009,null,-63.738905431611656,6.1994996678419385,1.5934726357902913,null,{"$f":"J14-F14","v":5.4334403927214225E-6},{"$f":"K14-G14","v":1.2168844900628528E-6},{"$f":"L14-H14","v":-1.3583600955158204E-7}]
["動摩擦係数","μ'",0,"[ND]",8.3999999999999991E-2,-66.528334247713644,5.4175195943911749,1.6632083561928408,null,-66.528328607748676,5.4175210859981267,1.6632082151937169,null,5.6399649679406139E-6,1.491606951731228E-6,-1.4099912393206182E-7]
["強制力","f",0,"[N]",9.5999999999999988E-2,-68.934738327334571,4.604350800443834,1.7233684581833641,null,-68.934732717682508,4.6043525775041783,1.7233683179420627,null,5.6096520637538561E-6,1.7770603442102129E-6,-1.4024130146061964E-7]
["強制力角振動数","Ω",0,"[rad/s]",0.10799999999999998,-70.944268868364929,3.7646736735510991,1.7736067217091229,null,-70.944263534364381,3.7646757426466864,1.7736065883591097,null,5.3340005479185493E-6,2.0690955873092776E-6,-1.3335001325387452E-7]
["初期位置","x0",1,"[m]",0.11999999999999998,-72.545356529771766,2.9033224328702434,1.8136339132442938,null,-72.545351722623522,2.9033247962991533,1.8136337930655881,null,4.8071482439127067E-6,2.3634289099128125E-6,-1.2017870565372846E-7]
["初期速度","x'0",10,"[m/s]",0.13199999999999998,-73.728783472462709,2.0252560805408715,1.8432195868115675,null,-73.728779446514054,2.0252587362223715,1.8432194861628513,null,4.0259486553395618E-6,2.6556815000411405E-6,-1.0064871625026228E-7]
[null,null,null,null,0.14399999999999999,-74.487736428558549,1.1355298515406147,1.8621934107139633,null,-74.48773343853388,1.1355327929607828,1.8621933359633469,null,2.9900246687475374E-6,2.941420168101061E-6,-7.4750616363417066E-8]
[null,"c/m",{"$f":"C12/C11","v":0},"[1/s]",0.156,-74.817845926982443,0.23926610950569438,1.8704461481745607,null,-74.817844225183777,0.23926932570439363,1.8704461056295945,null,1.7017986664313867E-6,3.2161986992518266E-6,-4.2544966216695457E-8]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,-74.717211449534986,-0.65837514392404117,1.8679302862383744,null,-74.717211283035937,-0.65837166832445093,1.8679302820758983,null,1.6649904921450798E-7,3.4755995902413517E-6,-4.1624761415448575E-9]
[null,"μ'g",{"$f":"C15*C10","v":0},"[s^2/m]",0.18000000000000002,-74.186412372625512,-1.5522259764509112,1.8546603093156373,null,-74.186413980482683,-1.5522222611751222,1.8546603495120673,null,-1.6078571718480816E-6,3.7152757890179799E-6,4.0196429962335856E-8]
[null,"f/m",{"$f":"C16/C11","v":0},"[N/m]",0.19200000000000003,-73.228504631665444,-2.4371402781239051,1.8307126157916358,null,-73.228508242171472,-2.4371363471317289,1.8307127060542869,null,-3.6105060274849166E-6,3.9309921762153976E-6,9.0262651131212124E-8]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,-71.849003127327862,-3.3080233887067436,1.7962250781831961,null,-71.849008955329353,-3.3080192700403841,1.7962252238832337,null,-5.828001491181567E-6,4.1186663595205175E-6,1.4570003759040162E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":6.324555320336759},"［rad/s］",0.21600000000000005,-70.05584997496419,-4.159861428837841,1.7513962493741044,null,-70.055858219268231,-4.1598571544292939,1.7513964554817056,null,-8.2443040412272239E-6,4.2744085471113635E-6,2.0610760120831628E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0},"[ND]",0.22800000000000006,-67.859368779974005,-4.9877501661157098,1.6964842194993497,null,-67.859379620865838,-4.9877457715556002,1.6964844905216458,null,-1.0840891832231137E-5,4.3945601095884967E-6,2.7102229616104978E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":0},"[1/s]",0.24000000000000007,-65.27220520237509,-5.786923249920978,1.631805130059377,null,-65.27221879926897,-5.7869187741904335,1.6318054699817244,null,-1.3596893879253003E-5,4.475730544406531E-6,3.3992234738100535E-7]
["振幅","A",{"$f":"SQRT(C18^2+(C19/C25)^2)","v":1.8708286933869707},"[m]",0.25200000000000006,-62.309254152757823,-6.5527796524204778,1.5577313538189452,null,-62.30927064200209,-6.5527751375879397,1.5577317660500523,null,-1.6489244266892911E-5,4.514832538049518E-6,4.1223110702759413E-7]
["初期位相","β",{"$f":"ATAN2(C25*C18,-C19)","v":-1.0068536854342678},"[rad]",0.26400000000000007,-58.987574038773587,-7.2809101577690898,1.4746893509693395,null,-58.987593531630054,-7.280905648654266,1.4746898382907514,null,-1.9492856466740704E-5,4.5091148237474954E-6,4.8732141189056222E-7]
[null,null,null,null,0.27600000000000008,-55.326288555860899,-7.967122747004745,1.3831572138965222,null,-55.326311136677106,-7.9671182908121869,1.3831577784169276,null,-2.2580816207096177E-5,4.4561925580666184E-6,5.6452040531063119E-7]
[null,null,null,null,0.28800000000000009,-51.346476587622554,-8.6074667324897778,1.2836619146905637,null,-51.34650231221454,-8.6074623784148052,1.2836625578053635,null,-2.5724591985465395E-5,4.3540749725679007E-6,6.4311479985867948E-7]
[null,null,null,null,0.3000000000000001,-47.071050849723939,-9.1982555029509587,1.1767762712430982,null,-47.071079743985031,-9.1982513017609016,1.1767769935996257,null,-2.8894261092204943E-5,4.201190057173676E-6,7.2235652748275925E-7]
[null,null,null,null,0.31200000000000011,-42.524625975987611,-9.7360877481696431,1.0631156493996901,null,-42.524658034737612,-9.7360837517635996,1.0631164508684403,null,-3.2058750001340286E-5,3.9964060434272142E-6,8.0146875025555175E-7]
["単振動解析解",null,null,null,0.32400000000000012,-37.733376806143951,-10.217867041126485,0.9433344201535987,null,-37.733411992231119,-10.21786330207699,0.94333529980577802,null,-3.51860871674603E-5,3.7390494949107733E-6,8.7965217931973427E-7]
["x''+ω^2x=0",null,null,"運動方程式",0.33600000000000013,-32.724887691108741,-10.640819664861725,0.81812219227771843,null,-32.724925934774866,-10.640816235941863,0.81812314836937172,null,-3.8243666125481468E-5,3.428919862713542E-6,9.5609165329246792E-7]
["x＝Acos{ωt＋α}",null,null,"変位",0.34800000000000014,-27.527993683372255,-11.002510581417562,0.68819984208430629,null,-27.528034881889752,-11.002507515117244,0.68820087204724378,null,-4.1198517497065268E-5,3.0663003176556458E-6,1.0299629374932451E-6]
["x'＝－Aωsin{ωt＋α}",null,null,"速度",0.36000000000000015,-22.172614526805006,-11.300857450925699,0.55431536317012509,null,-22.172658544392018,-11.300854798960936,0.55431646360980047,null,-4.4017587011779824E-5,2.6519647633449495E-6,1.1004396753833134E-6]
["x''＝－ω^2x",null,null,"加速度",0.37200000000000016,-16.68958240163904,-11.534142620128836,0.41723956004097595,null,-16.689629069657453,-11.534140432947876,0.41724072674143631,null,-4.6668018413242862E-5,2.1871809607887371E-6,1.166700460353276E-6]
["A=√{x0^2+(x0'/ω)^2}",null,null,"振幅",0.38400000000000017,-11.110464416338477,-11.701023011315375,0.27776161040846187,null,-11.110513533776585,-11.701021337605729,0.27776283834441462,null,-4.9117438107870726E-5,1.6737096455443634E-6,1.2279359527522793E-6]
["β=tan^(-1)(-x0'/(ωx0))",null,null,"初期位相",0.39600000000000019,-5.46738086831453,-11.800537854734406,0.13668452170786322,null,-5.4674322025548339,-11.800536740934731,0.13668580506387085,null,-5.1334240303901879E-5,1.113799674712368E-6,1.2833560076308537E-6]
[null,null,null,null,0.4080000000000002,0.20717968019833263,-11.832114219973658,-5.179492004958315E-3,null,0.20712639232869995,-11.832113709794516,-5.1781598082174989E-3,null,-5.3287869632684393E-5,5.101791415995649E-7,1.332196740816069E-6]
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{"sheet":"減衰振動","index":1,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,7],[3,5,3,7]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"減衰振動",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,J8:L8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,"解析解",null,null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-2*$C$28*G8-$C$25^2*H8","v":-60.000000000000007},{"$f":"-$C$28*H8-$C$29*$C$26*EXP(-$C$28*E8)*SIN($C$26*E8+$C$30)","v":10},{"$f":"$C$29*EXP(-$C$28*E8)*COS($C$26*E8+$C$30)","v":1},null,-60,10,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-63.145470663643209,9.2606967747381805,1.1156019278541709,null,-63.145470781440004,9.2606970419200003,1.11560191744,null,{"$f":"J9-F9","v":-1.1779679454093639E-7},2.671818197796938E-7,-1.0414170859007754E-8]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-65.857133189979734,8.4862442905290116,1.2221161152230426,null,-65.857133672516795,8.4862448205758696,1.2221161007841266,null,-4.8253706097511895E-7,5.3004685796054218E-7,-1.4438916062786689E-8]
["質量","m",10,"[kg]",3.6000000000000004E-2,-68.129849201022154,7.6818817136487816,1.3191521443431145,null,-68.129850282341309,7.6818824978745388,1.3191521321648059,null,-1.0813191551051204E-6,7.842257572221456E-7,-1.217830858379898E-8]
["粘性減衰係数","c",20,"[Ns/m]",4.8000000000000001E-2,-69.961099206075247,6.8528941167580859,1.4063827743139765,null,-69.961101105012901,6.8528951423276494,1.4063827705089402,null,-1.8989376542322134E-6,1.0255695634953099E-6,-3.8050362860531095E-9]
["バネ定数","k",400,"[N/m]",0.06,-71.350934829305118,6.0045813250805153,1.4835443044786021,null,-71.35093774739552,6.0045825752635817,1.4835443149217089,null,{"$f":"J13-F13","v":-2.9180904022041432E-6},{"$f":"K13-G13","v":1.2501830664035651E-6},{"$f":"L13-H13","v":1.0443106823743165E-8}]
["静止摩擦係数","μ",0,"[ND]",7.1999999999999995E-2,-72.301917543900913,5.1422274174492486,1.5504365677250602,null,-72.301921663498618,5.1422288719043037,1.5504365979922503,null,{"$f":"J14-F14","v":-4.1195977047436827E-6},1.4544550550610325E-6,3.026719008758505E-8]
["動摩擦係数","μ'",0,"[ND]",8.3999999999999991E-2,-72.819044581338247,4.2710710401911234,1.6069225625238996,null,-72.819050063970394,4.2710726752764998,1.606922617835435,null,-5.4826321473910866E-6,1.6350853764279805E-6,5.5311535351876273E-8]
["強制力","f",0,"[N]",9.5999999999999988E-2,-72.909662741358005,3.3962766834477067,1.6529277343615645,null,-72.909669726314348,3.3962784725563444,1.6529278195300412,null,-6.9849563431034767E-6,1.7891086376842225E-6,8.5168476715580255E-8]
["強制力角振動数","Ω",0,"[rad/s]",0.10799999999999998,-72.583370879895199,2.5229070605101933,1.68843891897187,null,-72.583379483061947,2.5229089744246473,1.6884390383553163,null,-8.6031667478891904E-6,1.9139144540325503E-6,1.1938344623985131E-7]
["初期位置","x0",1,"[m]",0.11999999999999998,-71.851911898169092,1.6558967211365647,1.7135029613973989,null,-71.851922211110775,1.6558987284007414,1.7135031188577323,null,-1.0312941682855126E-5,2.0072641766510912E-6,1.5746033343866372E-7]
["初期速度","x'0",10,"[m/s]",0.13199999999999998,-70.729055096348517,0.80002701969388612,1.7282250264240182,null,-70.729067185639536,0.80002908699792641,1.7282252252910923,null,-1.2089291018924087E-5,2.0673040402874321E-6,1.9886707414151772E-7]
[null,null,null,null,0.14399999999999999,-69.230469789544273,-4.0097451604299783E-2,1.7327666173188212,null,-69.230483696350234,-4.0095359029571863E-2,1.7327668603602344,null,-1.3906805961028113E-5,2.0925747279201823E-6,2.4304141321707107E-7]
[null,"c/m",{"$f":"C12/C11","v":2},"[1/s]",0.156,-67.373591112296793,-0.86007086504495767,1.7273433210596676,null,-67.373606852203238,-0.86006878302760881,1.7273436104564612,null,-1.5739906444878216E-5,2.0820173488589333E-6,2.8939679364015092E-7]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,-65.177478960201057,-1.6557065072812294,1.7122222993690877,null,-65.177496523285782,-1.6557044723053467,1.7122226366974118,null,-1.7563084725225053E-5,2.0349758826920805E-6,3.3732832416255576E-7]
[null,"μ'g",{"$f":"C15*C10","v":0},"[s^2/m]",0.18000000000000002,-62.66267103385519,-2.4230554001399449,1.6877195458533767,null,-62.662690384998299,-2.4230534489438118,1.6877199320721481,null,-1.935114310924746E-5,1.9511961331097893E-6,3.8621877140876393E-7]
[null,"f/m",{"$f":"C16/C11","v":0},"[N/m]",0.19200000000000003,-59.851030960980829,-3.1584231274462362,1.6541969303968325,null,-59.851052040404667,-3.1584212966249279,1.6541973658413633,null,-2.1079423838443745E-5,1.8308213083351177E-6,4.3544453087740465E-7]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,-56.765592477420142,-3.8583848146855022,1.6120590526697784,null,-56.76561520144999,-3.8583831403012088,1.6120595370513102,null,-2.272402984715427E-5,1.6743842934374698E-6,4.8438153177343679E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":6.2449979983983983},"［rad/s］",0.21600000000000005,-53.430400646877729,-4.5197982200921718,1.5617499271765514,null,-53.430424908912322,-4.5197967372953585,1.561750459587576,null,-2.4262034592936743E-5,1.4827968133346303E-6,5.3241102460077627E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0.15811388300841897},"[ND]",0.22800000000000006,-49.870351092884619,-5.1398149074801003,1.5037495226961202,null,-49.870376764564412,-5.1398136501445357,1.503750101621337,null,-2.5671679793504154E-5,1.257335564552875E-6,5.7892521687641363E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":1},"[1/s]",0.24000000000000007,-46.111028204683926,-5.7158894827459603,1.4385701792543959,null,-46.111055137243191,-5.7158884831203913,1.4385708025870994,null,-2.6932559265446798E-5,9.9962556898702815E-7,6.2333270345327207E-7]
["振幅","A",{"$f":"SQRT((C25*C18)^2+2*C28*C18*C19+C19^2)/C26","v":2.0254787341673333},"[m]",0.25200000000000006,-42.17854326176861,-6.2457868874204827,1.3667529259152391,null,-42.178571287556956,-6.2457861757996129,1.3667535909789046,null,-2.8025788346042191E-5,7.116208697866E-7,6.6506366547258722E-7]
["初期位相","β",{"$f":"ATAN2(C26*C18,-(C28*C18+C19))","v":-1.0544450085036257},"[rad]",0.26400000000000007,-38.099373399861292,-6.7275877538525313,1.2888637226891586,null,-38.099402334018691,-6.7275873582697052,1.2888644262639526,null,-2.8934157398907701E-5,3.9558282605156592E-7,7.0357479398097666E-7]
[null,null,null,null,0.27600000000000008,-33.900202314455925,-7.1596918375289551,1.2054896497378456,null,-33.900231956724518,-7.1596917834727476,1.2054903880917505,null,-2.9642268593477183E-5,5.4056207510200238E-8,7.3835390490550878E-7]
[null,null,null,null,0.28800000000000009,-29.607763566905632,-7.5408195526041375,1.1172350668028475,null,-29.60779370356093,-7.5408198627608281,1.1172358357270646,null,-3.0136655297496873E-5,-3.101566905527875E-7,7.689242171871058E-7]
[null,null,null,null,0.3000000000000001,-25.248687322723534,-7.8700116468851524,1.0247177654123458,null,-25.248717728607105,-7.8700123409087857,1.024718560260617,null,-3.0405883570949754E-5,-6.9402363322978999E-7,7.9484827120168688E-7]
[null,null,null,null,0.31200000000000011,-20.849351312563961,-8.146627062242878,0.92856513592624268,null,-20.84938175319893,-8.1466281565544154,0.92856595165769407,null,-3.044063496915328E-5,-1.0943115373862611E-6,8.1573145138680303E-7]
["減衰振動解析解",null,null,null,0.32400000000000012,-16.43573676358367,-8.3703390356519343,0.82941037087218838,null,-16.435766997354499,-8.3703405432686679,0.8294112020972958,null,-3.0233770829113382E-5,-1.5076167336758317E-6,8.3122510741162614E-7]
["x''+2γx'+ω^2x=0",null,null,"運動方程式",0.33600000000000013,-12.033290002877724,-8.5411295047616225,0.72788872531002413,null,-12.033319783255028,-8.541131435157876,0.72788956633926949,null,-2.9780377303723071E-5,-1.9303962535133223E-6,8.4102924535756074E-7]
["x＝Ae^(－γt)cos(ωdt＋β)",null,null,"変位",0.34800000000000014,-7.6667903857763484,-8.6592818900298205,0.62463385414589967,null,-7.6668194635681921,-8.6592842490295521,0.62463469904068236,null,-2.9077791843690193E-5,-2.3589997315554001E-6,8.4489478269222928E-7]
["x'＝－γx－Aωde^(－γt)sin(ωdt＋β)",null,null,"速度",0.36000000000000015,-3.3602251503299385,-8.725372332978651,0.52027424540718092,null,-3.3602532759404937,-8.7253751226804699,0.52027508803253586,null,-2.8125610555207459E-5,-2.7897018188838274E-6,8.4262535493540014E-7]
["x''＝－2γx'－ω^2x",null,null,"加速度",0.37200000000000016,0.86332825435265192,-8.7402594770268998,0.41542976749252863,null,0.86330132867555065,-8.7402626957616167,0.41543060157119205,null,-2.6925677101274914E-5,-3.2187347169809755E-6,8.3407866341422832E-7]
["A=√{(ωx0 )^2+2γx0x0'+x0'^2}/ωd ",null,null,"振幅",0.38400000000000017,4.9818118737512869,-8.7050728835946778,0.31070834733595165,null,4.9817863916976624,-8.7050765259153309,0.31070916650332497,null,-2.5482053624514833E-5,-3.6423206530855623E-6,8.191673733226601E-7]
["β=tan^(-1)(-(γx0+x0')/(x0ωd))",null,null,"初期位相",0.39600000000000019,8.9742885523927409,-8.6212001817411306,0.20670279527723795,null,8.9742647514188523,-8.6212042384451593,0.20670359313678666,null,-2.3800973888654653E-5,-4.0567040286987321E-6,7.9785954870681408E-7]
[null,null,null,null,0.4080000000000002,12.821034460057994,-8.4902730544704674,0.10398779122207349,null,12.821012569278501,-8.4902775126534333,0.10398856140070914,null,-2.1890779493105583E-5,-4.4581829659051664E-6,7.7017863564510236E-7]
[null,null,null,null,0.42000000000000021,16.503622521554977,-8.3141521690134841,3.1170454117997359E-3,null,16.50360275971493,-8.3141570121535686,3.1177816148051534E-3,null,-1.9761840047038959E-5,-4.843140084531683E-6,7.3620300541747674E-7]
[null,null,null,null,0.43200000000000022,20.004996491165155,-8.0949111618546077,-9.5379354186398438E-2,null,20.004979064707239,-8.0949163699268034,-9.5378658121340776E-2,null,-1.7426457915803439E-5,-5.2080721957281639E-6,6.9606505766206528E-7]
[null,null,null,null,0.44400000000000023,23.309535472231946,-7.8348197920248062,-0.1909973972045583,null,23.309520573473286,-7.8348253416436107,-0.1909967472546516,null,-1.4898758660564226E-5,-5.5496188045012218E-6,6.4994990670030894E-7]
[null,null,null,null,0.45600000000000024,26.403108741445031,-7.5363263782202212,-0.28326139962511465,null,26.403096546876867,-7.5363322428093333,-0.283260801531455,null,-1.2194568164147768E-5,-5.8645891121145155E-6,5.9809365965390882E-7]
[null,null,null,null,0.46800000000000025,29.273120795859192,-7.2020396366399604,-0.37172603806448173,null,29.273111464581419,-7.2020457866274024,-0.3717254972831654,null,-9.3312777735832242E-6,-6.149987441972371E-6,5.4078131633827908E-7]
[null,null,null,null,0.48000000000000026,31.908546598249394,-6.8347100370737053,-0.45597816310254952,null,31.908540270551057,-6.8347164401105305,-0.45597768475824985,null,-6.3276983368609763E-6,-6.4030368251977166E-6,4.78344299670308E-7]
[null,null,null,null,0.49200000000000027,34.299957052741675,-6.4372107947230361,-0.53563838658238994,null,34.299953848836957,-6.4372174159236932,-0.53563797542473923,null,-3.203904718418471E-6,-6.6212006570864901E-6,4.1115765070376398E-7]
[null,null,null,null,0.50400000000000023,36.439534797478572,-6.0125186145266296,-0.61036243921063271,null,36.439534816406749,-6.0125254167288711,-0.61036209957372523,null,1.8928176359622739E-8,-6.8022022414737648E-6,3.3963690748706199E-7]
[null,null,null,null,0.51600000000000024,38.321080454104262,-5.5636943033981705,-0.67984229618269798,null,38.321083772800357,-5.5637012474403456,-0.67984203194799164,null,3.3186960948228261E-6,-6.9440421750499581E-6,2.6423470633751833E-7]
[null,null,null,null,0.52800000000000025,39.940009524827317,-5.0938633638005779,-0.74380706993065404,null,39.94001619736936,-5.0938704088139479,-0.7438068844935366,null,6.6725420424518234E-6,-7.0450133700106221E-6,1.8543711743923552E-7]
[null,null,null,null,0.54000000000000026,41.293340176499271,-4.6061966794963558,-0.80202367043766387,null,41.293350233536131,-4.6062037832100664,-0.80202356667789998,null,1.0057036860189328E-5,-7.1037137105989245E-6,1.0375976389198627E-7]
[null,null,null,null,0.55200000000000027,42.379672197309297,-4.1038914011611221,-0.85429723487467624,null,42.379685645671977,-4.1038985202174025,-0.85429721513092938,null,1.3448362679469028E-5,-7.1190562804801516E-6,1.9743746859646194E-8]
[null,null,null,null,0.56400000000000028,43.199157455139414,-3.590152135856739,-0.90047132958564824,null,43.199174277637063,-3.5901592261337956,-0.90047139563423684,null,1.6822497649116031E-5,-7.0902770565872686E-6,-6.6048588598377478E-8]
[null,null,null,null,0.57600000000000029,43.753462227165478,-3.0681725401655884,-0.94042792867085734,null,43.753482382566332,-3.0681795571056885,-0.94042808170887393,null,2.0155400854093841E-5,-7.0169401000796938E-6,-1.530380165926104E-7]
[null,null,null,null,0.5880000000000003,44.045721807767592,-2.5411174121245645,-0.97408717458796146,null,44.045745230963149,-2.5411243110647983,-0.97408741522083886,null,2.3423195557370491E-5,-6.8989402337571448E-6,-2.4063287740183625E-7]
[null,null,null,null,0.60000000000000031,44.080487836085815,-2.0121053720037243,-1.001406927301959,null,44.08051443843577,-2.0121121085069071,-1.0014072555355489,null,2.6602349954885085E-5,-6.7365031828359179E-6,-3.28233589863558E-7]
[null,null,null,null,0.61200000000000032,43.863668815507481,-1.4841922164893515,-1.0223821095632193,null,43.863698485361219,-1.4841987466725906,-1.022382524800401,null,2.9669853738312213E-5,-6.5301832390396441E-6,-4.1523718175007218E-7]
[null,null,null,null,0.62400000000000033,43.402464324901374,-0.96035502499517822,-1.0370438568727753,null,43.40249692829083,-0.96036130585366786,-1.0370443579145874,null,3.2603389456653531E-5,-6.2808584896378861E-6,-5.0104181203991516E-7]
[null,null,null,null,0.63600000000000034,42.705293445446742,-0.443477090679955,-1.0454584816021706,null,42.705328826944069,-0.44348308040363787,-1.0454590666534198,null,3.5381497326625322E-5,-5.9897236828754252E-6,-5.8505124922447749E-7]
[null,null,null,null,0.64800000000000035,41.781717947388586,6.3666257663029358E-2,-1.047726261567866,null,41.781755931121126,6.3660599382238489E-2,-1.04772692824714,null,3.7983732539714765E-5,-5.6582807908683863E-6,-6.6667927400843041E-7]
[null,null,null,null,0.66000000000000036,40.642360797951206,0.55842088331588613,-1.0439800641145742,null,40.642401188764936,0.55841559498852023,-1.0439808094685494,null,4.0390813730084574E-5,-5.2883273659043439E-6,-7.4535397520669733E-7]
[null,null,null,null,0.67200000000000037,39.298820564949082,1.0382660662352019,-1.0343838174354869,null,39.298863149711138,1.0382611842923442,-1.0343846379573958,null,4.2584762056208092E-5,-4.8819428577484558E-6,-8.2052190886194865E-7]
[null,null,null,null,0.68400000000000039,37.763582300358173,1.5008256787861447,-1.0191308414482614,null,37.763626849387592,1.5008212373132424,-1.019131733100352,null,4.4549029418305963E-5,-4.4414729023500854E-6,-8.9165209060659834E-7]
[null,null,null,null,0.6960000000000004,36.049925494278916,1.9438782739094249,-0.99844205105244399,null,36.049971762894486,1.9438743043975908,-0.99844300929224183,null,4.6268615569999838E-5,-3.9695118341231961E-6,-9.5823979784359636E-7]
[null,null,null,null,0.70800000000000041,34.171829692386908,2.3653660541234109,-0.97256404501584304,null,34.171877422559994,2.3653625852398852,-0.97256506482599414,null,4.7730173086790728E-5,-3.4688835257590256E-6,-1.0198101511038615E-6]
[null,null,null,null,0.72000000000000042,32.143878369193772,2.7634026968795928,-0.94176709407382364,null,32.143927291293387,2.7633997542589448,-0.9417681699952819,null,4.892209961582239E-5,-2.9426206480387407E-6,-1.0759214582600762E-6]
[null,null,null,null,0.73200000000000043,29.981161645316519,3.1362800188761861,-0.90634304207672212,null,29.981211479933432,3.1362776249335576,-0.90634416824501363,null,4.9834616913102536E-5,-2.3939426285757293E-6,-1.1261682915097992E-6]
[null,null,null,null,0.74400000000000044,27.699178429580797,3.4824734689518264,-0.8666031341871111,null,27.699228889417189,3.4824716427194051,-0.8666043043713999,null,5.0459836391070212E-5,-1.8262324212869885E-6,-1.1701842888012237E-6]
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[null,null,null,null,5.8919999999999346,1.5575097119657655E-2,3.4455743816345953E-2,-2.1121646188087388E-3,null,1.5576933790726194E-2,3.4455921256326405E-2,-2.1122194075844751E-3,null,1.8366710685391308E-6,1.774399804518878E-7,-5.4788775736332868E-8]
[null,null,null,null,5.9039999999999342,-1.164565692131303E-3,3.4541846512575684E-2,-1.6979781833255014E-3,null,-1.1628583859862596E-3,3.4542045607273794E-2,-1.6980308207140333E-3,null,1.7073061450434412E-6,1.9909469810980296E-7,-5.2637388531879756E-8]
[null,null,null,null,5.9159999999999338,-1.7500634418547441E-2,3.4429409200162457E-2,-1.2839545995444366E-3,null,-1.7499063587574873E-2,3.4429628395262722E-2,-1.2840048300737643E-3,null,1.5708309725678826E-6,2.1919510026502387E-7,-5.0230529327751836E-8]
[null,null,null,null,5.9279999999999333,-3.3349749040111731E-2,3.4123779736446418E-2,-8.7244526081952745E-4,null,-3.3348320880713433E-2,3.4124017394369023E-2,-8.7249284770061532E-4,null,1.4281593982978791E-6,2.3765792260543872E-7,-4.7586881087870701E-8]
[null,null,null,null,5.9399999999999329,-4.8633296496036593E-2,3.363127816999361E-2,-4.6573149609876547E-4,null,-4.8632016273628759E-2,3.363153258083236E-2,-4.6577622220089906E-4,null,1.2802224078345414E-6,2.544108387500521E-7,-4.4726102133593824E-8]
[null,null,null,null,5.9519999999999325,-6.3277745319465742E-2,3.2959137732921431E-2,-6.6013253659428036E-5,null,-6.3276617356961759E-2,3.2959407125576941E-2,-6.6054922354803213E-5,null,1.1279625039828378E-6,2.6939265550945946E-7,-4.1668695375176733E-8]
[null,null,null,null,5.963999999999932,-7.7214943429408309E-2,3.2115442037723346E-2,3.2460148384904036E-4,null,-7.7213971101291135E-2,3.2115724591164435E-2,3.2456304797405679E-4,null,9.7232811717418155E-7,2.8255344108885083E-7,-3.8435874983569398E-8]
[null,null,null,null,5.9759999999999316,-9.0382378259045965E-2,3.1109058925869213E-2,7.0410651018268855E-4,null,-9.0381563990952568E-2,3.110935278045544E-2,7.0407146075104215E-4,null,8.1426809339646411E-7,2.938545862266051E-7,-3.5049431646393646E-8]
[null,null,null,null,5.9879999999999312,-0.10272339863379934,2.9949571423896568E-2,1.0706063946501548E-3,null,-0.10272274390749836,2.9949874692696832E-2,1.0705748630526176E-3,null,{"$f":"J507-F507","v":6.5472630098040163E-7},{"$f":"K507-G507","v":3.0326880026340652E-7},{"$f":"L507-H507","v":-3.1531597537203318E-8}]
[null,null,null,null,5.9999999999999307,-0.1141873980440085,2.8647206268357414E-2,1.4223246376823416E-3,null,-0.11418690340764924,2.8647517048399899E-2,1.422296732771236E-3,null,{"$f":"J508-F508","v":4.94636359260614E-7},3.1078004248535906E-7,-2.7904911105566463E-8]

{"sheet":"臨界減衰","index":2,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,7],[3,5,3,7]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"臨界減衰",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,J8:L8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,"解析解",null,null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"$C$9/500","v":1.2E-2},"[s]",0,{"$f":"-$C$25*(2*$C$30-$C$25*($C$29+$C$30*E8))*EXP(-$C$25*E8)","v":-166.49110640673518},{"$f":"($C$30-$C$25*($C$29+$C$30*E8))*EXP(-$C$25*E8)","v":10},{"$f":"($C$29+$C$30*E8)*EXP(-$C$25*E8)","v":1},null,-166.49110640673516,10,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-147.05981159601041,8.1207416046780576,1.1084913138529262,null,-147.05982571566469,8.1207434989338037,1.1084910678280206,null,{"$f":"J9-F9","v":-1.411965428133044E-5},1.8942557460377429E-6,-2.4602490555913903E-7]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-129.57950754995113,6.4627629034378735,1.1957826134981258,null,-129.57953342436335,6.4627663674703122,1.1957821649351925,null,-2.5874412216353448E-5,3.4640324386714383E-6,-4.4856293324180285E-7]
["質量","m",10,"[kg]",3.6000000000000004E-2,-113.86880736862938,5.00375715165901,1.2643932384558292,null,-113.86884292516268,5.0037619017788764,1.2643926252493685,null,-3.5556533305225457E-5,4.7501198663368882E-6,-6.1320646072005047E-7]
["粘性減衰係数","c=2√(mk) ",{"$f":"2*SQRT(C11*C13)","v":126.49110640673517},"[Ns/m]",4.8000000000000001E-2,-99.762416509694816,3.7234962486572662,1.3165875122574067,null,-99.762459936276031,3.7235020374817585,1.3165867673349001,null,-4.3426581214589532E-5,5.7888244922033039E-6,-7.4492250656810199E-7]
["バネ定数","k",400,"[N/m]",0.06,-87.109749424994689,2.6036460508893553,1.3543985614535639,null,-87.109799141608164,2.6036526633148682,1.3543977133363534,null,{"$f":"J13-F13","v":-4.9716613474970472E-5},{"$f":"K13-G13","v":6.6124255129196285E-6},{"$f":"L13-H13","v":-8.4811721046129662E-7}]
["静止摩擦係数","μ",0,"[ND]",7.1999999999999995E-2,-75.773662447904528,1.6275975779980671,1.3796500151328679,null,-75.773717080969647,1.627604827584858,1.3796490884388608,null,{"$f":"J14-F14","v":-5.4633065118991908E-5},7.2495867908806133E-6,-9.2669400708622618E-7]
["動摩擦係数","μ'",0,"[ND]",8.3999999999999991E-2,-65.629293328088622,0.78031277512499775,1.3939757675300382,null,-65.629351687444171,0.78032050085387772,1.3939747834239427,null,-5.8359355548986969E-5,7.7257288799703616E-6,-9.8410609550292349E-7]
["強制力","f",0,"[N]",9.5999999999999988E-2,-56.562998593180765,4.8183605395073874E-2,1.3988379709367977,null,-56.56305965142429,4.8191668759852223E-2,1.3988369475330558,null,-6.1058243524314548E-5,8.0633647783490137E-6,-1.0234037419731834E-6]
["強制力角振動数","Ω",0,"[rad/s]",0.10799999999999998,-48.471380636522476,-0.58109665205532635,1.3955434120323813,null,-48.471443510476796,-0.58108836965245758,1.395542364755483,null,-6.2873954320252778E-5,8.2824028687644713E-6,-1.0472768983138536E-6]
["初期位置","x0",1,"[m]",0.11999999999999998,-41.260397091668217,-1.1186509299495373,1.3852584118223057,null,-41.260461025767924,-1.11864252952944,1.3852573537287176,null,-6.3934099706841607E-5,8.4004200973097909E-6,-1.0580935880799558E-6]
["初期速度","x'0",10,"[m/s]",0.13199999999999998,-34.844545662504672,-1.5745256725125381,1.369022377517416,null,-34.844610013915286,-1.5745172396043323,1.3690213195829584,null,-6.4351410614449378E-5,8.4329082057355009E-6,-1.0579344575933902E-6]
[null,null,null,null,0.14399999999999999,-29.146118136815566,-1.9577887741823308,1.3477601238129111,null,-29.146182362115152,-1.9577803806867675,1.3477590751890498,null,-6.4225299585274342E-5,8.3934955632525288E-6,-1.048623861299447E-6]
[null,"c/m",{"$f":"C12/C11","v":12.649110640673516},"[1/s]",0.156,-24.094517824887866,-2.2766189525493501,1.322293071058471,null,-24.094581468157436,-2.2766106584024386,1.3222920393006616,null,-6.3643269569979566E-5,8.2941469115027644E-6,-1.0317578094110047E-6]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,-19.625635136925009,-2.5383872844545583,1.293349418671738,null,-19.625697819108048,-2.5383791391114241,1.2933484099426511,null,-6.2682183038731409E-5,8.1453431342026761E-6,-1.0087290869265075E-6]
[null,"μ'g",{"$f":"C15*C10","v":0},"[s^2/m]",0.18000000000000002,-15.681276446944116,-2.7497315733821641,1.2615733837702094,null,-15.681337856349032,-2.7497236171392272,1.2615724030204025,null,-6.1409404915835353E-5,7.9562429369239851E-6,-9.8074980692253177E-7]
[null,"f/m",{"$f":"C16/C11","v":0},"[N/m]",0.19200000000000003,-12.20864178955523,-2.9166241604811467,1.2275335873185691,null,-12.208701673386557,-2.9166164256529545,1.2275326384469125,null,-5.9883831326601467E-5,7.7348281921629791E-6,-9.4887165658086303E-7]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,-9.1598473023802427,-3.0444337403356858,1.191730663052146,null,-9.1599054591951514,-3.044426252301172,1.1917297490480925,null,-5.8156814908727483E-5,7.4880345137806614E-6,-9.1400405355379633E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":0},"［rad/s］",0.21600000000000005,-6.4914886634653701,-3.137981695605796,1.1546041579897841,null,-6.4915449364620343,-3.1379744737373145,1.1546032810593645,null,-5.6272996664219477E-5,7.2218684814551182E-6,-8.7693041961323104E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":1},"[ND]",0.22800000000000006,-4.1642420822692277,-3.2015934215333282,1.1165387874424195,null,-4.1642963533225625,-3.2015864800205196,1.1165379491196645,null,-5.4271053334886687E-5,6.9415128085559274E-6,-8.3832275499240438E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":6.324555320336759},"[1/s]",0.24000000000000007,-2.1424996868699817,-3.2391450717399866,1.0778701020125356,null,-2.1425518712383607,-3.2391384203193434,1.0778693032578543,null,-5.2184368378949131E-5,6.6514206431556033E-6,-7.987546812859847E-7]
["振幅","A1",{"$f":"C18","v":1},"[m]",0.25200000000000006,-0.39403641095792102,-3.2541061204433985,1.0388896191234833,null,-0.39408645259195652,-3.2540997650433625,1.0388888604103785,null,-5.0041634035491445E-5,6.3554000360177554E-6,-7.5871310478703435E-7]
[" 〝","A2",{"$f":"C25*C18+C19","v":16.32455532033676},null,0.26400000000000007,1.1102942761725634,-3.249578102918409,0.99984946707880873,null,1.1102464087815349,-3.2495720462288427,0.99984874847017324,null,-4.7867391028466599E-5,6.0566895663249909E-6,-7.1860863548600662E-7]
[null,null,null,null,0.27600000000000008,2.3968382333276508,-3.2283298654885777,0.96096658549570046,null,2.3967925508155261,-3.2283241074625963,0.96096590671081072,null,-4.568251212466734E-5,5.7580259813505563E-6,-6.7878488974049134E-7]
[null,null,null,null,0.28800000000000009,3.48939433940135,-3.192829628322408,0.92242652215173226,null,3.4893508347663698,-3.1928241666177697,0.9224258826249504,null,-4.350463498026258E-5,5.4617046383320655E-6,-6.3952678186485201E-7]
[null,null,null,null,0.3000000000000001,4.4094460626484056,-3.1452741386231726,0.88438686280112977,null,4.409404714099054,-3.1452689689896847,0.88438626173321466,null,-4.1348549351560848E-5,5.1696334879558492E-6,-6.0106791510694535E-7]
[null,null,null,null,0.31200000000000011,5.1763727858533688,-3.0876151682500064,0.84698032732906836,null,5.1763335593104358,-3.0876102848688016,0.84697976373191264,null,-3.9226542932979669E-5,4.8833812047455183E-6,-5.6359715572273927E-7]
["臨界減衰解析解",null,null,null,0.32400000000000012,5.8076426095763232,-3.0215835882166591,0.81031756269548705,null,5.8076054608660428,-3.0215789839965628,0.81031703543100875,null,-3.7148710280376918E-5,4.6042200962936874E-6,-5.2726447830053758E-7]
["x''+2γx'+ω^2x=0",null,null,"運動方程式",0.33600000000000013,6.3189882120558645,-2.9487112327219469,0.77448966045102086,null,6.3189530888276089,-2.9487068995576644,0.77448916826486647,null,-3.5123228255606875E-5,4.3331642824995242E-6,-4.921861543882855E-7]
["x=(A1+A2t)e^(-ωt)",null,null,"変位",0.34800000000000014,6.7245672125418601,-2.8703507472251717,0.73957042416623098,null,6.7245340559404418,-2.8703466762215295,0.73956996571687916,null,-3.3156601418227183E-5,4.0710036421920393E-6,-4.5844935181449387E-7]
["x'={A2-ω(A1+A2t)}e^(-ωt)",null,null,"速度",0.36000000000000015,7.0371083638567562,-2.7876935984547364,0.70561840988236246,null,7.0370771099763232,-2.7876897801207638,0.70561798376615115,null,-3.1253880433013137E-5,3.8183339725605947E-6,-4.2611621131616317E-7]
["x''=-ω{2A2-ω(A1+A2t)}e^(-ωt)",null,null,"加速度",0.37200000000000016,7.2680447889651463,-2.701786409004181,0.67267876064991827,null,7.2680153701090155,-2.7017828334204763,0.67267836542247439,null,-2.9418856130725146E-5,3.5755837046735905E-6,-3.9522744388342801E-7]
["A1=x0",null,null,"振幅１",0.38400000000000017,7.4276353744589034,-2.6135457652126184,0.64078485435448085,null,7.4276077202270088,-2.6135424221750228,0.64078448854896775,null,-2.765423189465821E-5,3.34303759563781E-6,-3.6580551310283482E-7]
["A2=ωx0+x0'",null,null,"振幅２",0.39600000000000019,7.5250753403941726,-2.5237716342404166,0.60995978232265691,null,7.5250493786178119,-2.5237685133827683,0.60995944446522354,null,-2.5961776360716726E-5,3.1208576483088279E-6,-3.378574333634532E-7]
[null,null,null,null,0.4080000000000002,7.5685969201642225,-2.4331595145397458,0.58021767464141205,null,7.5685725777056518,-2.4331566054381515,0.58021736326417805,null,-2.4342458570636438E-5,2.9091015942839249E-6,-3.11377233996879E-7]
[null,null,null,null,0.42000000000000021,7.5655610054287905,-2.3423114331941082,0.55156488669895087,null,7.5655382088612306,-2.3423087254549282,0.5515646003508281,null,-2.2796567559879577E-5,2.7077391799856798E-6,-2.8634812276884247E-7]
[null,null,null,null,0.43200000000000022,7.5225405389682356,-2.2517458937798951,0.52400106015339831,null,7.5225192151505489,-2.2517433771134159,0.52400079740902195,null,-2.1323817686713653E-5,2.5166664792131144E-6,-2.6274437636697456E-7]
[null,null,null,null,0.44400000000000023,7.4453963721582168,-2.1619068694113719,0.4975200703464584,null,7.4453764487167433,-2.1619045336929013,0.49751982981346132,null,-1.9923441473501668E-5,2.3357184706362943E-6,-2.4053299707560427E-7]
[null,null,null,null,0.45600000000000024,7.3393462430785217,-2.0731719273994518,0.47211087109338779,null,7.3393276488073766,-2.0731697627194237,0.47211065141823683,null,-1.8594271145033758E-5,2.1646800281160949E-6,-2.1967515095866474E-7]
[null,null,null,null,0.46800000000000025,7.2090274756298172,-1.9858595644212009,0.44775824678934179,null,7.2090101408196432,-1.9858575611256488,0.44775804666191904,null,-1.7334810173963433E-5,2.0032955521109841E-6,-2.0012742274477802E-7]
[null,null,null,null,0.48000000000000026,7.058553949020359,-1.900235824202924,0.42444348086734635,null,7.0585378057245656,-1.9002339729256033,0.42444329902444988,null,-1.6143295793469292E-5,1.8512773207746136E-6,-1.8184289646283602E-7]
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[null,null,null,null,5.9759999999999316,1.4387321889214475E-13,-2.3377056644511944E-14,3.7956439264394719E-15,null,1.4387459644449944E-13,-2.3377281453798866E-14,3.7956805785691863E-15,null,1.3775523546990015E-18,-2.2480928692235219E-19,3.6652129714319471E-20]
[null,null,null,null,5.9879999999999312,1.3363779948526595E-13,-2.1712745223982764E-14,3.5252279291411895E-15,null,1.3363908204191873E-13,-2.1712954514617849E-14,3.525262048734849E-15,null,{"$f":"J507-F507","v":1.2825566527774158E-18},{"$f":"K507-G507","v":-2.0929063508527801E-19},{"$f":"L507-H507","v":3.4119593659493322E-20}]
[null,null,null,null,5.9999999999999307,1.2413000379414017E-13,-2.0166839488092124E-14,3.2740645040860204E-15,null,1.2413119789411002E-13,-2.0167034329467298E-14,3.2740962658395716E-15,null,{"$f":"J508-F508","v":1.19409996985563E-18},-1.9484137517351506E-19,3.1761753551215953E-20]

{"sheet":"過減衰","index":3,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,7],[3,5,3,7]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"過減衰",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,J8:L8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,"解析解",null,null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"EXP(-$C$28*E8)*(($C$28-$C$31)^2*$C$29*EXP($C$31*E8)+($C$28+$C$31)^2*$C$30*EXP(-$C$31*E8))","v":-419.47331922020544},{"$f":"-EXP(-$C$28*E8)*(($C$28-$C$31)*$C$29*EXP($C$31*E8)+($C$28+$C$31)*$C$30*EXP(-$C$31*E8))","v":10},{"$f":"EXP(-$C$28*E8)*($C$29*EXP($C$31*E8)+$C$30*EXP(-$C$31*E8))","v":1},null,-419.47331922020555,10,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-268.99152704002131,5.9355684829050723,1.0938134918334663,null,-269.04682824453539,5.9370686969368469,1.0937727939508703,null,{"$f":"J9-F9","v":-5.5301204514080382E-2},1.5002140317745827E-3,-4.0697882595974733E-5]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-172.30979462250789,3.3303969843575372,1.1482528706249049,null,-172.38086691497222,3.3323250373031965,1.1482005663092074,null,-7.1072292464322118E-2,1.928052945659342E-3,-5.2304315697471182E-5]
["質量","m",10,"[kg]",3.6000000000000004E-2,-110.19596158429701,1.6627574150076065,1.1774688512800626,null,-110.26446738111437,1.6646158439179093,1.1774184357326778,null,-6.8505796817362352E-2,1.8584289103027452E-3,-5.0415547384830006E-5]
["粘性減衰係数","c>2√(mk)",{"$f":"3*(2*SQRT(C11*C13))","v":379.4733192202055},"[Ns/m]",4.8000000000000001E-2,-70.292847720518978,0.59742647713099906,1.1905526723456392,null,-70.351542814092284,0.59901876075460858,1.1905094768054933,null,-5.8695093573305712E-2,1.592283623609525E-3,-4.319554014586835E-5]
["バネ定数","k",400,"[N/m]",0.06,-44.660632857681868,-8.0984785767087689E-2,1.1933447350954822,null,-44.70777915106266,-7.9705798617116186E-2,1.1933100386824023,null,{"$f":"J13-F13","v":-4.7146293380791349E-2},{"$f":"K13-G13","v":1.2789871499715028E-3},{"$f":"L13-H13","v":-3.4696413079959854E-5}]
["静止摩擦係数","μ",0,"[ND]",7.1999999999999995E-2,-28.197769676167816,-0.51086854993095832,1.1895967027229812,null,-28.234124709232688,-0.50988230867220286,1.1895699479395727,null,{"$f":"J14-F14","v":-3.6355033064872089E-2},9.8624125875546031E-4,-2.6754783408522442E-5]
["動摩擦係数","μ'",0,"[ND]",8.3999999999999991E-2,-17.626377642279831,-0.78114449858588686,1.1817181802294705,null,-17.653632698273068,-0.78040512199586898,1.1816981224073813,null,-2.7255055993236965E-2,7.393765900178817E-4,-2.0057822089247779E-5]
["強制力","f",0,"[N]",9.5999999999999988E-2,-10.840331266008645,-0.94894491809442238,1.171256476216308,null,-10.860347149848309,-0.94840192615762564,1.1712417459308839,null,-2.0015883839663573E-2,5.4299193679674396E-4,-1.4730285424091605E-5]
["強制力角振動数","Ω",0,"[rad/s]",0.10799999999999998,-6.4863892377300392,-1.0509778486817085,1.1592048626086486,null,-6.5008590548488598,-1.0505853107432337,1.1591942138505362,null,-1.4469817118820671E-2,3.9253793847482399E-4,-1.0648758112408174E-5]
["初期位置","x0",1,"[m]",0.11999999999999998,-3.6950586100933855,-1.1108282148463831,1.1462006396803666,null,-3.7053899412342801,-1.1105479459804002,1.146193036566767,null,-1.0331331140894573E-2,2.8026886598286893E-4,-7.6031135995968668E-6]
["初期速度","x'0",10,"[m/s]",0.13199999999999998,-1.9076677818214296,-1.1436489982496822,1.1326523980172112,null,-1.914970502963655,-1.1434508896811268,1.132647023755577,null,-7.3027211422254101E-3,1.981085685553996E-4,-5.3742616341612148E-6]
[null,null,null,null,0.14399999999999999,-0.76525622957499417,-1.1591754425602621,1.1188217876066089,null,-0.77037551128812254,-1.1590365664565931,1.1188180202093874,null,-5.1192817131283652E-3,1.3887610366891678E-4,-3.767397221521307E-6]
[null,"c/m",{"$f":"C12/C11","v":37.947331922020552},"[1/s]",0.156,-3.7183166416197157E-2,-1.1636617611381912,1.104876056532254,null,-4.0746913603697976E-2,-1.163565083661489,1.1048734339044959,null,-3.5637471875008195E-3,9.6677476702167198E-5,-2.6226277580754243E-6]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,0.42474331896102496,-1.1611255237565246,1.0909218083539449,null,0.42227712447052568,-1.1610586207511417,1.0909199934524108,null,-2.466194490499285E-3,6.6903005382812353E-5,-1.8149015341695218E-6]
[null,"μ'g",{"$f":"C15*C10","v":0},"[s^2/m]",0.18000000000000002,0.71573952632947113,-1.1541472084484574,1.0770266919884401,null,0.71404157085135722,-1.1541011462750448,1.0770254424608041,null,-1.6979554781139106E-3,4.6062173412630969E-5,-1.2495276360269258E-6]
[null,"f/m",{"$f":"C16/C11","v":0},"[N/m]",0.19200000000000003,0.89698351025110523,-1.1443839349613445,1.0632333378988759,null,0.89581967696881293,-1.1443523624862866,1.0632324814511671,null,-1.1638332822923037E-3,3.157247505791716E-5,-8.5644770875248355E-7]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,1.0077828481367355,-1.1328995521923075,1.0495683123303308,null,1.0069882355153581,-1.1328779959578568,1.0495677276062723,null,-7.9461262137736632E-4,2.1556234450770262E-5,-5.8472405850551468E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":{"$error":"#NUM!"}},"［rad/s］",0.21600000000000005,1.0733927589825265,-1.1203767281097234,1.0360478705076137,null,1.0728521107530753,-1.120362061437566,1.0360474726864355,null,-5.4064822945121271E-4,1.4666672157437333E-5,-3.9782117822184659E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":3},"[ND]",0.22800000000000006,1.1100394551949104,-1.1072532230938037,1.0226816530818186,null,1.1096727377125433,-1.1072432748268579,1.0226813832641815,null,-3.6671748236716262E-4,9.9482669457806594E-6,-2.698176371218608E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":18.973665961010276},"[1/s]",0.24000000000000007,1.1281477813575631,-1.0938094490826029,1.0094750610605605,null,1.1278997287892096,-1.0938027199663147,1.0094748785745358,null,-2.48052568353474E-4,6.7291162881844002E-6,-1.824860247356952E-7]
["振幅","A1",{"$f":"(1/(2*$C$31))*(($C$28+$C$31)*$C$18+$C$19)","v":1.3098385830773844},"[m]",0.25200000000000006,1.1344150589660713,-1.0802247285370958,0.99643078163014187,null,1.1342476923932452,-1.0802201882772546,0.99643065852578172,null,-1.67366572826122E-4,4.5402598412014328E-6,-1.2310436015017245E-7]
[" 〝","A2",{"$f":"(1/(2*$C$31))*((-$C$28+$C$31)*$C$18-$C$19)","v":-0.30983858307738432},"[rad]",0.26400000000000007,1.1331435874039617,-1.0666134421983262,0.98354976840462061,null,1.1330309175402533,-1.0666103857561056,0.98354968555552658,null,-1.1266986370839227E-4,3.0564422206502684E-6,-8.284909402966889E-8]
["過減衰固有角振動数","ωd'＝ω√(ζ^2-1)",{"$f":"C25*SQRT(C27^2-1)","v":17.888543819998318},"［rad/s］",0.27600000000000008,1.1270968115765536,-1.0530482548533477,0.97083187113119862,null,1.127021119829827,-1.05304620155776,0.97083181549763609,null,-7.5691746726613829E-5,2.0532955877783365E-6,-5.5633562534573855E-8]
[null,null,null,null,0.28800000000000009,1.1180494325371975,-1.0395750383753948,0.95827624016352952,null,1.1179986788675009,-1.0395736616035178,0.95827620288478654,null,-5.0753669696534942E-5,1.3767718769486237E-6,-3.7278742981428081E-8]
[null,null,null,null,0.3000000000000001,1.1071408682398094,-1.0262224600407899,0.94588158621901341,null,1.1071068954199319,-1.0262215385028588,0.94588156129186607,null,-3.3972819877492455E-5,9.2153793107563331E-7,-2.492714734625423E-8]
[null,null,null,null,0.31200000000000011,1.0951023614497879,-1.0130081431442084,0.93364634715383021,null,1.0950796575684763,-1.0130075273127308,0.93364633052182544,null,-2.2703881311647578E-5,6.1583147759058932E-7,-1.6632004773420306E-8]
["過減衰解析解",null,null,null,0.32400000000000012,1.0824029025508559,-0.99994262522499611,0.92156879499596733,null,1.0823877521063565,-0.99994221430557395,0.92156878392468666,null,-1.5150444499401061E-5,4.1091942215576438E-7,-1.1071280670016392E-8]
["x''+2γx'+ω^2x=0",null,null,"運動方程式",0.33600000000000013,1.0693429887364931,-0.98703190120099837,0.9096471045940201,null,1.0693328926282391,-0.98703162739783257,0.90964709724423587,null,-1.0096108254087355E-5,2.738031658067186E-7,-7.3497842256742274E-9]
["x=e^-(γt){A1e^(ωd't)+A2e^(-ωd't)}",null,null,"変位",0.34800000000000014,1.0561148666745297,-0.9742790572690524,0.89787939760468716,null,1.0561081473198968,-0.97427887507252775,0.89787939274175266,null,-6.7193546329225029E-6,1.8219652464512848E-7,-4.8629344995276824E-9]
["x'=-e^(-γt){(γ-ωd')A1e^(ωd't)+(γ+ωd')A2e^(-ωd't)}",null,null,"速度",0.36000000000000015,1.0428412399018039,-0.96168532060025036,0.88626377063626649,null,1.0428367732381645,-0.96168519951667186,0.88626376743288848,null,-4.4666636394019577E-6,1.2108357849704987E-7,-3.2033780072993068E-9]
["x''=e^(-γt){(γ-ωd')^2A1e^(ωd't)+(γ+ωd')^2A2e^(-ωd't)}",null,null,"加速度",0.37200000000000016,1.0296001392293366,-0.94925073366928092,0.87479831321351043,null,1.0295971733442286,-0.94925065330066671,0.8747983111162756,null,-2.9658851079528148E-6,8.0368614208126132E-8,-2.0972348302450428E-9]
["A1={1/(2ωd')}{(γ+ωd')x0+x'0}",null,null,"振幅１",0.38400000000000017,1.0164409025106624,-0.936974587402718,0.86348111920396375,null,1.0164389352111485,-0.93697453412549025,0.863481117843235,null,-1.9672995139607963E-6,5.3277227740622379E-8,-1.360728751897966E-9]
["A2={1/(2ωd')}{(-γ+ωd')x0-x'0}",null,null,"振幅２",0.39600000000000019,1.0033944419381426,-0.92485569936360046,0.85231029404462177,null,1.0033931382969072,-0.924855664091773,0.85231029317385865,null,-1.3036412354061611E-6,3.5271827458771554E-8,-8.7076312826894764E-10]
[null,null,null,null,0.4080000000000002,0.99047984092381791,-0.91289259236928166,0.84128395927167854,null,0.99047897786538641,-0.91289256905119398,0.8412839587266584,null,-8.6305843149947492E-7,2.3318087682966393E-8,-5.4502014013024791E-10]
[null,null,null,null,0.42000000000000021,0.97770859264114729,-0.90108360913656838,0.83040025531891137,null,0.97770802177215188,-0.90108359374654023,0.8304002549903734,null,-5.7086899540870206E-7,1.5390028140771506E-8,-3.2853797460319356E-10]
[null,null,null,null,0.43200000000000022,0.9650873232720002,-0.88942698582422952,0.81965734320505801,null,0.96508694599295097,-0.88942697568739293,0.81965734302038629,null,-3.7727904922402189E-7,1.0136836592344878E-8,-1.8467172235858698E-10]
[null,null,null,null,0.44400000000000023,0.95261954163763185,-0.8779208991675207,0.8090534055087758,null,0.95261929250531097,-0.87792089250847405,0.80905340541975712,null,-2.4913232088419335E-7,6.6590466474281129E-9,-8.9018681315167214E-11]
[null,null,null,null,0.45600000000000024,0.94030676325679152,-0.86656349664639842,0.79858664688727121,null,0.94030659887872758,-0.86656349228793705,0.79858664686192282,null,-1.6437806393820864E-7,4.3584613695912822E-9,-2.5348390053636649E-11]
[null,null,null,null,0.46800000000000025,0.92814923245805214,-0.85535291575394023,0.78825529430312047,null,0.92814912409006212,-0.85535291291623672,0.78825529432023789,null,-1.0836799002600372E-7,2.8377035166116116E-9,1.7117418593670664E-11]
[null,null,null,null,0.48000000000000026,0.91614638623274569,-0.84428729626283217,0.77805759706495659,null,0.91614631485104425,-0.84428729442975747,0.77805759711049138,null,-7.1381701438610889E-8,1.8330746920369734E-9,4.5534798154278633E-11]
[null,null,null,null,0.49200000000000027,0.90429715215090389,-0.83336478799441915,0.7679918267499406,null,0.90429710517562256,-0.83336478682465742,0.76799182681458888,null,-4.6975281331462782E-8,1.169761731922847E-9,6.4648286723922865E-11]
[null,null,null,null,0.50400000000000023,0.89260013965977592,-0.82258355569948183,0.75805627705160894,null,0.89260010877881868,-0.82258355496749203,0.75805627712920598,null,-3.0880957235801532E-8,7.3198980210520403E-10,7.7597039904730991E-11]
[null,null,null,null,0.51600000000000024,0.88105376287932213,-0.81194178208463785,0.74824926358108312,null,0.88105374260466718,-0.81194178164149455,0.74824926366754652,null,-2.0274654954910432E-8,4.4314329983308198E-10,8.6463392001689954E-11]
[null,null,null,null,0.52800000000000025,0.86965631938424348,-0.80143766964871044,0.7385691236396511,null,0.86965630609502398,-0.80143766939613859,0.73856912373227046,null,-1.3289219502610194E-8,2.5257185232163692E-10,9.2619356628631522E-11]
[null,null,null,null,0.54000000000000026,0.85840604070764992,-0.79106944175582894,0.72901421597420757,null,0.85840603201653565,-0.79106944162901882,0.72901421607118266,null,-8.691114272707523E-9,1.2681011796189523E-10,9.6975094621143398E-11]
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{"sheet":"過減衰 (双曲線)","index":4,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,7],[3,5,3,7]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"過減衰（双曲線関数）",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,J8:L8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,"解析解",null,null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"($C$31^2-$C$28^2)*H8-2*$C$28*G8","v":-419.47331922020561},{"$f":"-$C$28*H8+$C$31*EXP(-$C$28*E8)*(($C$29+$C$30)*SINH($C$31*E8)+($C$29-$C$30)*COSH($C$31*E8))","v":10.000000000000004},{"$f":"EXP(-$C$28*E8)*(($C$29+$C$30)*COSH($C$31*E8)+($C$29-$C$30)*SINH($C$31*E8))","v":1},null,-419.47331922020555,10,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},{"$f":"EXP(-$C$28*E9)*(($C$28-$C$31)^2*$C$29*EXP($C$31*E9)+($C$28+$C$31)^2*$C$30*EXP(-$C$31*E9))","v":-268.99152704002131},{"$f":"-EXP(-$C$28*E9)*(($C$28-$C$31)*$C$29*EXP($C$31*E9)+($C$28+$C$31)*$C$30*EXP(-$C$31*E9))","v":5.9355684829050723},{"$f":"EXP(-$C$28*E9)*($C$29*EXP($C$31*E9)+$C$30*EXP(-$C$31*E9))","v":1.0938134918334663},null,-269.04682824453539,5.9370686969368469,1.0937727939508703,null,{"$f":"J9-F9","v":-5.5301204514080382E-2},1.5002140317745827E-3,-4.0697882595974733E-5]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-172.30979462250789,3.3303969843575372,1.1482528706249049,null,-172.38086691497222,3.3323250373031965,1.1482005663092074,null,-7.1072292464322118E-2,1.928052945659342E-3,-5.2304315697471182E-5]
["質量","m",10,"[kg]",3.6000000000000004E-2,-110.19596158429701,1.6627574150076065,1.1774688512800626,null,-110.26446738111437,1.6646158439179093,1.1774184357326778,null,-6.8505796817362352E-2,1.8584289103027452E-3,-5.0415547384830006E-5]
["粘性減衰係数","c>2√(mk)",{"$f":"3*(2*SQRT(C11*C13))","v":379.4733192202055},"[Ns/m]",4.8000000000000001E-2,-70.292847720518978,0.59742647713099906,1.1905526723456392,null,-70.351542814092284,0.59901876075460858,1.1905094768054933,null,-5.8695093573305712E-2,1.592283623609525E-3,-4.319554014586835E-5]
["バネ定数","k",400,"[N/m]",0.06,-44.660632857681868,-8.0984785767087689E-2,1.1933447350954822,null,-44.70777915106266,-7.9705798617116186E-2,1.1933100386824023,null,{"$f":"J13-F13","v":-4.7146293380791349E-2},{"$f":"K13-G13","v":1.2789871499715028E-3},{"$f":"L13-H13","v":-3.4696413079959854E-5}]
["静止摩擦係数","μ",0,"[ND]",7.1999999999999995E-2,-28.197769676167816,-0.51086854993095832,1.1895967027229812,null,-28.234124709232688,-0.50988230867220286,1.1895699479395727,null,{"$f":"J14-F14","v":-3.6355033064872089E-2},9.8624125875546031E-4,-2.6754783408522442E-5]
["動摩擦係数","μ'",0,"[ND]",8.3999999999999991E-2,-17.626377642279831,-0.78114449858588686,1.1817181802294705,null,-17.653632698273068,-0.78040512199586898,1.1816981224073813,null,-2.7255055993236965E-2,7.393765900178817E-4,-2.0057822089247779E-5]
["強制力","f",0,"[N]",9.5999999999999988E-2,-10.840331266008645,-0.94894491809442238,1.171256476216308,null,-10.860347149848309,-0.94840192615762564,1.1712417459308839,null,-2.0015883839663573E-2,5.4299193679674396E-4,-1.4730285424091605E-5]
["強制力角振動数","Ω",0,"[rad/s]",0.10799999999999998,-6.4863892377300392,-1.0509778486817085,1.1592048626086486,null,-6.5008590548488598,-1.0505853107432337,1.1591942138505362,null,-1.4469817118820671E-2,3.9253793847482399E-4,-1.0648758112408174E-5]
["初期位置","x0",1,"[m]",0.11999999999999998,-3.6950586100933855,-1.1108282148463831,1.1462006396803666,null,-3.7053899412342801,-1.1105479459804002,1.146193036566767,null,-1.0331331140894573E-2,2.8026886598286893E-4,-7.6031135995968668E-6]
["初期速度","x'0",10,"[m/s]",0.13199999999999998,-1.9076677818214296,-1.1436489982496822,1.1326523980172112,null,-1.914970502963655,-1.1434508896811268,1.132647023755577,null,-7.3027211422254101E-3,1.981085685553996E-4,-5.3742616341612148E-6]
[null,null,null,null,0.14399999999999999,-0.76525622957499417,-1.1591754425602621,1.1188217876066089,null,-0.77037551128812254,-1.1590365664565931,1.1188180202093874,null,-5.1192817131283652E-3,1.3887610366891678E-4,-3.767397221521307E-6]
[null,"c/m",{"$f":"C12/C11","v":37.947331922020552},"[1/s]",0.156,-3.7183166416197157E-2,-1.1636617611381912,1.104876056532254,null,-4.0746913603697976E-2,-1.163565083661489,1.1048734339044959,null,-3.5637471875008195E-3,9.6677476702167198E-5,-2.6226277580754243E-6]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,0.42474331896102496,-1.1611255237565246,1.0909218083539449,null,0.42227712447052568,-1.1610586207511417,1.0909199934524108,null,-2.466194490499285E-3,6.6903005382812353E-5,-1.8149015341695218E-6]
[null,"μ'g",{"$f":"C15*C10","v":0},"[s^2/m]",0.18000000000000002,0.71573952632947113,-1.1541472084484574,1.0770266919884401,null,0.71404157085135722,-1.1541011462750448,1.0770254424608041,null,-1.6979554781139106E-3,4.6062173412630969E-5,-1.2495276360269258E-6]
[null,"f/m",{"$f":"C16/C11","v":0},"[N/m]",0.19200000000000003,0.89698351025110523,-1.1443839349613445,1.0632333378988759,null,0.89581967696881293,-1.1443523624862866,1.0632324814511671,null,-1.1638332822923037E-3,3.157247505791716E-5,-8.5644770875248355E-7]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,1.0077828481367355,-1.1328995521923075,1.0495683123303308,null,1.0069882355153581,-1.1328779959578568,1.0495677276062723,null,-7.9461262137736632E-4,2.1556234450770262E-5,-5.8472405850551468E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":{"$error":"#NUM!"}},"［rad/s］",0.21600000000000005,1.0733927589825265,-1.1203767281097234,1.0360478705076137,null,1.0728521107530753,-1.120362061437566,1.0360474726864355,null,-5.4064822945121271E-4,1.4666672157437333E-5,-3.9782117822184659E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":3},"[ND]",0.22800000000000006,1.1100394551949104,-1.1072532230938037,1.0226816530818186,null,1.1096727377125433,-1.1072432748268579,1.0226813832641815,null,-3.6671748236716262E-4,9.9482669457806594E-6,-2.698176371218608E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":18.973665961010276},"[1/s]",0.24000000000000007,1.1281477813575631,-1.0938094490826029,1.0094750610605605,null,1.1278997287892096,-1.0938027199663147,1.0094748785745358,null,-2.48052568353474E-4,6.7291162881844002E-6,-1.824860247356952E-7]
["振幅","A1",{"$f":"(1/(2*$C$31))*(($C$28+$C$31)*$C$18+$C$19)","v":1.3098385830773844},"[m]",0.25200000000000006,1.1344150589660713,-1.0802247285370958,0.99643078163014187,null,1.1342476923932452,-1.0802201882772546,0.99643065852578172,null,-1.67366572826122E-4,4.5402598412014328E-6,-1.2310436015017245E-7]
[" 〝","A2",{"$f":"(1/(2*$C$31))*((-$C$28+$C$31)*$C$18-$C$19)","v":-0.30983858307738432},"[rad]",0.26400000000000007,1.1331435874039617,-1.0666134421983262,0.98354976840462061,null,1.1330309175402533,-1.0666103857561056,0.98354968555552658,null,-1.1266986370839227E-4,3.0564422206502684E-6,-8.284909402966889E-8]
["過減衰固有角振動数","ωd'＝ω√(ζ^2-1)",{"$f":"C25*SQRT(C27^2-1)","v":17.888543819998318},"［rad/s］",0.27600000000000008,1.1270968115765536,-1.0530482548533477,0.97083187113119862,null,1.127021119829827,-1.05304620155776,0.97083181549763609,null,-7.5691746726613829E-5,2.0532955877783365E-6,-5.5633562534573855E-8]
[null,null,null,null,0.28800000000000009,1.1180494325371975,-1.0395750383753948,0.95827624016352952,null,1.1179986788675009,-1.0395736616035178,0.95827620288478654,null,-5.0753669696534942E-5,1.3767718769486237E-6,-3.7278742981428081E-8]
[null,null,null,null,0.3000000000000001,1.1071408682398094,-1.0262224600407899,0.94588158621901341,null,1.1071068954199319,-1.0262215385028588,0.94588156129186607,null,-3.3972819877492455E-5,9.2153793107563331E-7,-2.492714734625423E-8]
[null,null,null,null,0.31200000000000011,1.0951023614497879,-1.0130081431442084,0.93364634715383021,null,1.0950796575684763,-1.0130075273127308,0.93364633052182544,null,-2.2703881311647578E-5,6.1583147759058932E-7,-1.6632004773420306E-8]
["過減衰解析解（双曲線関数）",null,null,null,0.32400000000000012,1.0824029025508559,-0.99994262522499611,0.92156879499596733,null,1.0823877521063565,-0.99994221430557395,0.92156878392468666,null,-1.5150444499401061E-5,4.1091942215576438E-7,-1.1071280670016392E-8]
["x''+2γx'+ω^2x=0",null,null,"運動方程式",0.33600000000000013,1.0693429887364931,-0.98703190120099837,0.9096471045940201,null,1.0693328926282391,-0.98703162739783257,0.90964709724423587,null,-1.0096108254087355E-5,2.738031658067186E-7,-7.3497842256742274E-9]
["x=e^(-γt){(A1+A2)cosh(ωd't)+(A1-A2)sinh(ωd't)}",null,null,"変位",0.34800000000000014,1.0561148666745297,-0.9742790572690524,0.89787939760468716,null,1.0561081473198968,-0.97427887507252775,0.89787939274175266,null,-6.7193546329225029E-6,1.8219652464512848E-7,-4.8629344995276824E-9]
["x'=-γx+ωd'e^(-γt){(A1+A2)sinh(ωd't)+(A1-A2)cosh(ωd't)}",null,null,"速度",0.36000000000000015,1.0428412399018039,-0.96168532060025036,0.88626377063626649,null,1.0428367732381645,-0.96168519951667186,0.88626376743288848,null,-4.4666636394019577E-6,1.2108357849704987E-7,-3.2033780072993068E-9]
["x''=-γx'-γ(γx+x')+ωd'^2x=(ωd'^2-γ^2)x-2γx'",null,null,"加速度",0.37200000000000016,1.0296001392293366,-0.94925073366928092,0.87479831321351043,null,1.0295971733442286,-0.94925065330066671,0.8747983111162756,null,-2.9658851079528148E-6,8.0368614208126132E-8,-2.0972348302450428E-9]
["A1={1/(2ωd')}{(γ+ωd')x0+x'0}",null,null,"振幅１",0.38400000000000017,1.0164409025106624,-0.936974587402718,0.86348111920396375,null,1.0164389352111485,-0.93697453412549025,0.863481117843235,null,-1.9672995139607963E-6,5.3277227740622379E-8,-1.360728751897966E-9]
["A2={1/(2ωd')}{(-γ+ωd')x0-x'0}",null,null,"振幅２",0.39600000000000019,1.0033944419381426,-0.92485569936360046,0.85231029404462177,null,1.0033931382969072,-0.924855664091773,0.85231029317385865,null,-1.3036412354061611E-6,3.5271827458771554E-8,-8.7076312826894764E-10]
[null,null,null,null,0.4080000000000002,0.99047984092381791,-0.91289259236928166,0.84128395927167854,null,0.99047897786538641,-0.91289256905119398,0.8412839587266584,null,-8.6305843149947492E-7,2.3318087682966393E-8,-5.4502014013024791E-10]
[null,null,null,null,0.42000000000000021,0.97770859264114729,-0.90108360913656838,0.83040025531891137,null,0.97770802177215188,-0.90108359374654023,0.8304002549903734,null,-5.7086899540870206E-7,1.5390028140771506E-8,-3.2853797460319356E-10]
[null,null,null,null,0.43200000000000022,0.9650873232720002,-0.88942698582422952,0.81965734320505801,null,0.96508694599295097,-0.88942697568739293,0.81965734302038629,null,-3.7727904922402189E-7,1.0136836592344878E-8,-1.8467172235858698E-10]
[null,null,null,null,0.44400000000000023,0.95261954163763185,-0.8779208991675207,0.8090534055087758,null,0.95261929250531097,-0.87792089250847405,0.80905340541975712,null,-2.4913232088419335E-7,6.6590466474281129E-9,-8.9018681315167214E-11]
[null,null,null,null,0.45600000000000024,0.94030676325679152,-0.86656349664639842,0.79858664688727121,null,0.94030659887872758,-0.86656349228793705,0.79858664686192282,null,-1.6437806393820864E-7,4.3584613695912822E-9,-2.5348390053636649E-11]
[null,null,null,null,0.46800000000000025,0.92814923245805214,-0.85535291575394023,0.78825529430312047,null,0.92814912409006212,-0.85535291291623672,0.78825529432023789,null,-1.0836799002600372E-7,2.8377035166116116E-9,1.7117418593670664E-11]
[null,null,null,null,0.48000000000000026,0.91614638623274569,-0.84428729626283217,0.77805759706495659,null,0.91614631485104425,-0.84428729442975747,0.77805759711049138,null,-7.1381701438610889E-8,1.8330746920369734E-9,4.5534798154278633E-11]
[null,null,null,null,0.49200000000000027,0.90429715215090389,-0.83336478799441915,0.7679918267499406,null,0.90429710517562256,-0.83336478682465742,0.76799182681458888,null,-4.6975281331462782E-8,1.169761731922847E-9,6.4648286723922865E-11]
[null,null,null,null,0.50400000000000023,0.89260013965977592,-0.82258355569948183,0.75805627705160894,null,0.89260010877881868,-0.82258355496749203,0.75805627712920598,null,-3.0880957235801532E-8,7.3198980210520403E-10,7.7597039904730991E-11]
[null,null,null,null,0.51600000000000024,0.88105376287932213,-0.81194178208463785,0.74824926358108312,null,0.88105374260466718,-0.81194178164149455,0.74824926366754652,null,-2.0274654954910432E-8,4.4314329983308198E-10,8.6463392001689954E-11]
[null,null,null,null,0.52800000000000025,0.86965631938424348,-0.80143766964871044,0.7385691236396511,null,0.86965630609502398,-0.80143766939613859,0.73856912373227046,null,-1.3289219502610194E-8,2.5257185232163692E-10,9.2619356628631522E-11]
[null,null,null,null,0.54000000000000026,0.85840604070764992,-0.79106944175582894,0.72901421597420757,null,0.85840603201653565,-0.79106944162901882,0.72901421607118266,null,-8.691114272707523E-9,1.2681011796189523E-10,9.6975094621143398E-11]
[null,null,null,null,0.55200000000000027,0.84730112467665442,-0.78083534321952064,0.71958292052298389,null,0.84730111901059857,-0.78083534317575587,0.71958292062311591,null,-5.6660558467314104E-9,4.3764769586118746E-11,1.0013201379166503E-10]
[null,null,null,null,0.56400000000000028,0.83633975607595523,-0.77073364057395821,0.71027363815628342,null,0.83633975239910185,-0.77073364058509286,0.71027363825876777,null,-3.6768533773212653E-9,-1.113464875857062E-11,1.0248435433624081E-10]
[null,null,null,null,0.57600000000000029,0.82552011981328466,-0.7607626221455227,0.70108479041523963,null,0.82552011744390796,-0.7607626221930216,0.70108479051953509,null,-2.3693766948440498E-9,-4.7498893707142997E-11,1.0429546115631183E-10]
[null,null,null,null,0.5880000000000003,0.81484040926857559,-0.75092059799742683,0.69201481925054897,null,0.81484040775825406,-0.75092059806908362,0.69201481935628617,null,-1.5103215345035892E-9,-7.1656791611474091E-11,1.0573719677609006E-10]
[null,null,null,null,0.60000000000000031,0.80429883154993265,-0.74120589979405838,0.68306218676237795,null,0.80429883060386231,-0.74120589988183339,0.68306218686930009,null,-9.4607033318538925E-10,-8.7775009482982114E-11,1.0692213781027249E-10]
[null,null,null,null,0.61200000000000032,0.79389361076355691,-0.73161688061504548,0.67422537494222168,null,0.79389361018802873,-0.73161688071364384,0.67422537505014835,null,-5.7552818066852751E-10,-9.859835170544784E-11,1.0792666760295333E-10]
[null,null,null,null,0.62400000000000033,0.78362299000897606,-0.72215191473830309,0.66550288541720271,null,0.78362298967674704,-0.72215191484423524,0.66550288552600423,null,-3.3222902207086236E-10,-1.0593215193921424E-10,1.0880152334635795E-10]
[null,null,null,null,0.63600000000000034,0.77348523255661072,-0.71280939740440274,0.65689323919709308,null,0.77348523238414302,-0.7128093975153631,0.65689323930667087,null,-1.7246770678269741E-10,-1.1096035201774157E-10,1.0957779128517586E-10]
[null,null,null,null,0.64800000000000035,0.76347862250131127,-0.70358774457017947,0.64839497642422772,null,0.76347862243377307,-0.70358774468464347,0.64839497653450606,null,-6.7538197257022148E-11,-1.1446399383885364E-10,1.1027834201371434E-10]
[null,null,null,null,0.66000000000000036,0.75360146508054482,-0.69448539265666775,0.64000665612642027,null,0.75360146508195669,-0.69448539277362442,0.64000665623733954,null,1.4118706204158116E-12,-1.1695666657374204E-10,1.1091927376583044E-10]
[null,null,null,null,0.67200000000000037,0.74385208677841663,-0.68550079829460142,0.63172685597292244,null,0.74385208682518922,-0.68550079841337364,0.63172685608443002,null,4.677258580443322E-11,-1.1877221428591156E-10,1.1150758094657931E-10]
[null,null,null,null,0.68400000000000039,0.73422883529337446,-0.67663243806953188,0.62355417203342955,null,0.73422883537002903,-0.67663243818966534,0.62355417214548148,null,7.6654571579126696E-11,-1.2013345873640446E-10,1.1205192329555302E-10]
[null,null,null,null,0.6960000000000004,0.72473007941962664,-0.66787880826790524,0.61548721854015276,null,0.72473007951601431,-0.66787880838909164,0.61548721865271028,null,9.6387675618814228E-11,-1.2118639425295896E-10,1.1255751886096732E-10]
[null,null,null,null,0.70800000000000041,0.71535420887437406,-0.65923842462490911,0.60752462765292492,null,0.71535420898383251,-0.65923842474693373,0.60752462776595073,null,1.0945844231002866E-10,-1.2202461263655096E-10,1.1302581093275421E-10]
[null,null,null,null,0.72000000000000042,0.70609963409147047,-0.65070982207460393,0.59966504922731179,null,0.70609963420962885,-0.65070982219731555,0.59966504934077203,null,1.1815837197559631E-10,-1.22711618644189E-10,1.1346024120229004E-10]
[null,null,null,null,0.73200000000000043,0.69696478599475753,-0.64229155450266917,0.59190715058571486,null,0.69696478611874824,-0.64229155462595966,0.59190715069957844,null,1.2399070659085965E-10,-1.2329048892922856E-10,1.1386358522713635E-10]
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{"sheet":"動摩擦","index":5,"n_rows":508,"n_cols":18,"rows_kept":508,"cut":false,"hidden":false,"merged":[[3,6,3,7],[1,5,1,8]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"摩擦力が作用する振動",null,null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,K8:M8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,null,"マクロは標準モジュール-Module6 の中。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,null,"解析解",null,null,null,null,"数値積分",null,null,null,null,"理論値との差"]
[null,null,null,null,"時間","振幅","加速度","速度","変位",null,"加速度","速度","変位","変位x",null,"加速度","速度","変位"]
[null,null,null,null,"t","An","理論値y''","理論値y'","理論値y",null,"y''","y'","y","理論値x",null,"y''","y'","y"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]","[m]",null,"[m/s^2]","[m/s]","[m]"]
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["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},{"$f":"IF($C$18-(2*INT(($C$25*E9)/PI())+1)*$C$31<=$C$32,0,$C$18-(2*INT(($C$25*E9)/PI())+1)*$C$31)","v":0.92649999999999999},{"$f":"-F9*$C$25^2*COS($C$25*E9)","v":-36.953318421908527},{"$f":"-F9*$C$25*SIN($C$25*E9)","v":-0.44429319173932452},{"$f":"IF(F9>0,F9*COS($C$25*E9)-IF(H9<=0,-$C$31,$C$31),I8)","v":0.99733296054771292},null,-36.953318431743995,-0.4442930688000003,0.9973329607935999,0.92383296079359989,null,-9.8354675515111012E-9,1.2293932422080545E-7,2.4588697744576393E-10]
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["質量","m",10,"[kg]",3.6000000000000004E-2,0.92649999999999999,-36.103547407093558,-1.3226626991012167,0.97608868517733882,null,-36.103547788967894,-1.3226623352293134,0.97608869472419735,0.90258869472419734,null,-3.8187433659686576E-7,3.6387190327502594E-7,9.5468585259439465E-9]
["粘性減衰係数","c",0,"[Ns/m]",4.8000000000000001E-2,0.92649999999999999,-35.365350302419557,-1.7516820344111668,0.95763375756048863,null,-35.36535104277413,-1.7516815567493513,0.95763377606935318,0.88413377606935317,null,-7.4035457231502733E-7,4.776618154345158E-7,1.8508864552124749E-8]
["バネ定数","k",400,"[N/m]",0.06,0.92649999999999999,-34.423546539352664,-2.170616523323627,0.93408866348381636,null,-34.423547748453878,-2.1706159390597741,0.93408869371134695,0.86058869371134694,null,-1.2091012138171209E-6,5.8426385285414995E-7,3.0227530589677087E-8]
["静止摩擦係数","μ",0.8,"[ND]",7.1999999999999995E-2,0.92649999999999999,-33.283558304168999,-2.5770542612301717,0.90558895760422486,null,-33.283560087126773,-2.5770535795261407,0.90558900217816918,0.83208900217816917,null,-1.7829577743100344E-6,6.8170403100253907E-7,4.457394431334194E-8]
["動摩擦係数","μ'",0.3,"[ND]",8.3999999999999991E-2,0.92649999999999999,-31.951948777868843,-2.9686552902637851,0.87229871944672088,null,-31.9519512333862,-2.9686545221692917,0.87229878083465506,0.79879878083465505,null,-2.4555173574469791E-6,7.6809449334191982E-7,6.1387934180423542E-8]
["強制力","f",0,"[N]",9.5999999999999988E-2,0.92649999999999999,-30.436384350396462,-3.3431650709879022,0.83440960875991133,null,-30.436387569573991,-3.3431642293358816,0.83440968923934977,0.76090968923934976,null,-3.219177528990258E-6,8.4165202052233212E-7,8.0479438446801055E-8]
["強制力角振動数","Ω",0,"[rad/s]",0.10799999999999998,0.92649999999999999,-28.745590483426014,-3.6984274623114084,0.79213976208565018,null,-28.745594548631445,-3.6984265615957117,0.79213986371578615,0.71863986371578614,null,-4.0652054309475716E-6,9.0071569669447626E-7,1.0163013597352943E-7]
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["初期速度","x'0",0,"[m/s]",0.13199999999999998,0.92649999999999999,-24.87820442098511,-4.3431513466251594,0.69545511052462761,null,-24.878210385227273,-4.3431503771967943,0.69545525963068189,0.62195525963068188,null,-5.9642421632588594E-6,9.6942836513846942E-7,1.4910605428131163E-7]
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[null,"c/m",{"$f":"C12/C11","v":0},"[1/s]",0.156,0.92649999999999999,-20.438724215976997,-4.888001003537223,0.58446810539942473,null,-20.438732279223977,-4.8880000395408754,0.58446830698059948,0.51096830698059947,null,-8.0632469803276763E-6,9.6399634763599806E-7,2.0158117475244097E-7]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,0.92649999999999999,-18.035900199867978,-5.1189596208126185,0.52439750499669935,null,-18.035909356201916,-5.1189586897530841,0.52439773390504796,0.45089773390504795,null,-9.1563339381650621E-6,9.3105953435923539E-7,2.2890834860955778E-7]
[null,"μ'g",{"$f":"C15*C10","v":2.94},"[s^2/m]",0.18000000000000002,0.92649999999999999,-15.529239254691383,-5.3204471808546145,0.46173098136728447,null,-15.529249515179908,-5.3204463037737275,0.46173123787949771,0.3882312378794977,null,-1.0260488524593825E-5,8.7708088702953546E-7,2.5651221324807238E-7]
[null,"f/m",{"$f":"C16/C11","v":0},"[N/m]",0.19200000000000003,0.92649999999999999,-12.93317281840573,-5.4913036722832302,0.39682932046014313,null,-12.933184180056108,-5.4913028706315741,0.3968296045014027,0.32332960450140269,null,-1.1361650377850196E-5,8.0165165616818967E-7,2.8404125956837944E-7]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,0.92649999999999999,-10.262647057457507,-5.6305454340011742,0.3300661764364376,null,-10.262659502910987,-5.6305447294201629,0.33006648757277468,0.25656648757277467,null,-1.244545348022541E-5,7.0458101131265494E-7,3.1113633708335087E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":6.324555320336759},"［rad/s］",0.21600000000000005,0.92649999999999999,-7.5330368181776342,-5.7373708183626677,0.26182592045444081,null,-7.5330503155327388,-5.7373702324619247,0.26182625788831848,0.18832625788831847,null,-1.3497355104696851E-5,5.8590074303310757E-7,3.3743387767293243E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0},"[ND]",0.22800000000000006,0.92649999999999999,-4.7600571101668159,-5.8111648064479091,0.19250142775417037,null,-4.7600716129341532,-5.8111643605798031,0.19250179032335382,0.11900179032335381,null,-1.4502767337276623E-5,4.4586810599156479E-7,3.6256918345412004E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":0},"[1/s]",0.24000000000000007,0.92649999999999999,-1.9596726312807571,-5.8515025488719763,0.12249181578201893,null,-1.9596880784709492,-5.8515022639051741,0.12249220196177373,4.8992201961773715E-2,null,-1.5447190192086069E-5,2.8496680215539527E-7,3.8617975479937616E-7]
["振幅","A",{"$f":"SQRT(C18^2+(C19/C25)^2)","v":1},"[m]",0.25200000000000006,0.92649999999999999,0.85199414489874792,-5.8581518117428857,5.2200146377531315E-2,null,0.85197782855352555,-5.8581517078368437,5.2200554286161861E-2,-2.1299445713838148E-2,null,-1.6316345222366913E-5,1.0390604199272957E-7,4.079086305466828E-7]
["初期位相","β",{"$f":"ATAN2(C25*C18,-C19)","v":0},"[rad]",0.26400000000000007,0.92649999999999999,3.6587557899448289,-5.8310743136868561,-1.7968894748620692E-2,null,3.658738693636157,-5.8310744100691378,-1.7968467340903932E-2,-9.1468467340903942E-2,null,-1.7096308671860072E-5,-9.6382281711271389E-8,4.2740771676041955E-7]
["振動中心","d＝μ' mg/k",{"$f":"C15*C11*C10/C13","v":7.350000000000001E-2},"[m]",0.27600000000000008,0.92649999999999999,6.444453115426815,-5.7704259462431926,-8.7611327885670331E-2,null,6.4444353417838833,-5.7704262609915196,-8.7610883544597076E-2,-0.16111088354459707,null,-1.7773642931651068E-5,-3.1474832695721489E-7,4.4434107325519445E-7]
["振動限界","h=(μ+μ') mg/k",{"$f":"(C14+C15)*C11*C10/C13","v":0.26950000000000002},"[m]",0.28800000000000009,{"$f":"IF($C$18-(2*INT(($C$25*E32)/PI())+1)*$C$31<=$C$32,0,$C$18-(2*INT(($C$25*E32)/PI())+1)*$C$31)","v":0.92649999999999999},9.193048205167285,-5.6765558763599584,-0.15632620512918205,null,9.193029869641828,-5.6765564261908574,-0.15632574674104568,-0.22982574674104569,null,-1.8335525457047197E-5,-5.4983089903259952E-7,4.5838813636511766E-7]
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["摩擦力が作用する振動の解析解",null,null,null,0.32400000000000012,0.92649999999999999,17.059589864327013,-5.2019563475219384,-0.35298974660817517,null,17.059570652268906,-5.2019576863071011,-0.35298926630672262,-0.42648926630672263,null,-1.921205810617721E-5,-1.3387851627300051E-6,4.8030145255451018E-7]
["x''+ω^2x=0",null,null,"運動方程式",0.33600000000000013,0.92649999999999999,19.505024499751901,-4.9824632945564149,-0.41412561249379737,null,19.505005299266404,-4.9824649177835294,-0.41412513248166005,-0.48762513248166006,null,-1.9200485496639885E-5,-1.6232271145000254E-6,4.8001213731607706E-7]
["y=An cosωt-sign(y')d","変位",null,"変位",0.34800000000000014,0.92649999999999999,21.838164111196956,-4.7342850258841347,-0.47245410277992372,null,21.838145088425822,-4.7342869406496657,-0.47245362721064549,-0.54595362721064555,null,-1.9022771134302729E-5,-1.9147655310192135E-6,4.755692782354437E-7]
["y'=-An ωsinωt","速度",null,"速度",0.36000000000000015,0.92649999999999999,24.045576263926225,-4.4588503623011055,-0.52763940659815545,null,24.045557591712516,-4.4588525733091702,-0.52763893979281284,-0.60113893979281285,null,-1.8672213709436392E-5,-2.2110080646342567E-6,4.6680534260268303E-7]
["y''=-An ω^2  cosωt","加速度",null,"加速度",0.37200000000000016,0.92649999999999999,26.114552365821464,-4.1577450460940035,-0.57936380914553642,null,26.114534222349818,-4.1577475555387435,-0.57936335555874541,-0.65286335555874542,null,-1.8143471645970521E-5,-2.5094447400064723E-6,4.5358679101603627E-7]
["An=y0-(2n+1)d","振幅",null,"振幅",0.38400000000000017,0.92649999999999999,28.033180833742676,-3.8327026115480267,-0.62732952084356675,null,28.033163401106567,-3.8327054190150567,-0.62732908502766416,-0.70082908502766417,null,-1.7432636109759869E-5,-2.8074670299638171E-6,4.3581590258856551E-7]
["n=int{((ωt+β))/π}","半周期の番号",null,"半周期番号",0.39600000000000019,0.92649999999999999,29.790415671320257,-3.4855944045813656,-0.67126039178300623,null,29.790399134026615,-3.4855975069693663,-0.67125997835066531,-0.74475997835066532,null,-1.6537293642926443E-5,-3.1023880007197135E-6,4.1343234091772985E-7]
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{"sheet":"減衰振動＋外力","index":6,"n_rows":508,"n_cols":22,"rows_kept":508,"cut":false,"hidden":false,"merged":[[3,5,3,7],[3,8,3,10],[3,11,3,13],[1,5,1,13]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,"運動方程式",null,"減衰振動＋強制振動",null,null,null,null,null,null,null,null,null,"マクロで計算➡",null,{"$f":"exe(\"振動シミュレーション\",\"ForcedOscillation\",C8:C19,P8:R8)","v":"振動シミュレーション"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,"微分方程式",null,null,null,null,null,null,null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["    ダンパ ＋バネ  ＋  動摩擦    ＋ 外力",null,null,null,null,"減衰振動解析解",null,null,"強制振動解析解",null,null,"（減衰+強制）解析解",null,null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位","加速度","速度","変位","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x","理論値x''","理論値x'","理論値x","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,"赤太字は単振動からの変更データ",null,null,"[s]","[m/s^2]","[m/s]","[m]","[m/s^2]","[m/s]","[m]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-2*$C$28*G8-$C$25^2*H8","v":-65},{"$f":"-$C$28*H8-$C$29*$C$26*EXP(-$C$28*E8)*SIN($C$26*E8+$C$30)","v":11.5},{"$f":"$C$29*EXP(-$C$28*E8)*COS($C$26*E8+$C$30)","v":1.0499999999999998},{"$f":"-$C$31*$C$17^2*SIN($C$17*E8+$C$32)","v":5.0000000000000018},{"$f":"$C$31*$C$17*COS($C$17*E8+$C$32)","v":-1.5000000000000002},{"$f":"$C$31*SIN($C$17*E8+$C$32)","v":-5.0000000000000017E-2},{"$f":"F8+I8","v":-60},{"$f":"G8+J8","v":10},{"$f":"H8+K8","v":0.99999999999999978},null,-60,10,1,null,{"$f":"P8-L8","v":0},{"$f":"Q8-M8","v":0},{"$f":"R8-N8","v":0}]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-68.723480302914055,10.697184353543996,1.1832277898956514,6.7597262886031251,-1.4293568501363398,-6.7597262886031254E-2,{"$f":"F9+I9","v":-61.963754014310929},{"$f":"G9+J9","v":9.2678275034076556},{"$f":"H9+K9","v":1.1156305270096201},null,-61.963754490989302,9.2678277326038163,1.1156305274667715,null,{"$f":"P9-L9","v":-4.7667837321796469E-7},{"$f":"Q9-M9","v":2.2919616071703786E-7},{"$f":"R9-N9","v":4.5715142782398743E-10}]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-71.967713766094946,9.852553855650898,1.3065651513698284,8.422229270667172,-1.338155649064477,-8.4222292706671711E-2,-63.545484495427772,8.5143982065864208,1.2223428586631566,null,-63.545485654625416,8.5143986575208359,1.222342865096377,null,-1.1591976445401997E-6,4.509344151415462E-7,6.4332204008366034E-9]
["質量","m",10,"[kg]",3.6000000000000004E-2,-74.725609922737732,8.9719049639406574,1.41954499987141,9.9635976175160259,-1.2277081188793575,-9.9635976175160262E-2,-64.762012305221702,7.7441968450612997,1.3199090236962499,null,-64.762014333821611,7.7441975071942775,1.3199090413045989,null,-2.0285999084990181E-6,6.6213297778006108E-7,1.7608349001108081E-8]
["粘性減衰係数","c",20,"[Ns/m]",4.8000000000000001E-2,-76.993013077645116,8.0611015749313406,1.5217702481945605,11.361662247018668,-1.0996027963981851,-0.11361662247018667,-65.631350830626445,6.961498778533155,1.4081536257243739,null,-65.631353895438977,6.9614996385133585,1.4081536593456774,null,-3.064812531761163E-6,8.5998020349364879E-7,3.3621303519026924E-8]
["バネ定数","k",400,"[N/m]",0.06,-78.768656351698141,7.1260400668352304,1.6129144054506916,12.596315175473926,-0.9556821856669997,-0.12596315175473927,{"$f":"F13+I13","v":-66.172341176224222},{"$f":"G13+J13","v":6.1703578811682309},{"$f":"H13+K13","v":1.4869512536959524},null,-66.172345423146425,6.1703589231091076,1.4869513077719643,null,-4.2469222023555631E-6,1.0419408766892957E-6,5.4076011890558107E-8]
["静止摩擦係数","μ",0,"[ND]",7.1999999999999995E-2,-80.054100382526229,6.1726149865616726,1.6927217602350715,13.649798725276574,-0.79801625772560625,-0.13649798725276574,-66.404301657249661,5.3745987288360659,1.5562237729823059,null,-66.4043072106887,5.3745999345952225,1.5562238515303246,null,-5.5534390384082144E-6,1.205759156519548E-6,7.8548018755952853E-8]
["動摩擦係数","μ'",0,"[ND]",8.3999999999999991E-2,-80.853657393957747,5.2066855608459885,1.7610071568066439,14.506960928769432,-0.62887267877653275,-0.14506960928769433,-66.346696465188316,4.5778128820694555,1.6159375475189495,null,-66.346703427736216,4.5778142315279799,1.6159376541097212,null,-6.9625479000023915E-6,1.349458524479985E-6,1.0659077176455867E-7]
["強制力","f",100,"[N]",9.5999999999999988E-2,-81.174301413165836,4.2340432024690617,1.8176553752056925,15.15547345487726,-0.4506841949581859,-0.15155473454877261,-66.018827958288568,3.7833590075108758,1.6661006406569199,null,-66.018836410633412,3.7833604788498647,1.6661007783985915,null,-8.4523448435902537E-6,1.4713389888676431E-6,1.3774167162416973E-7]
["強制力角振動数","Ω",10,"[rad/s]",0.10799999999999998,-81.025565474754558,3.2603801728169368,1.8626201282280168,15.586008924142915,-0.2660136428181365,-0.15586008924142913,-65.439556550611641,2.9943665299988003,1.7067600389865878,null,-65.439566551668406,2.9943680999707589,1.7067602105144093,null,-1.0001056764963323E-5,1.5699719586592664E-6,1.715278215019822E-7]
["初期位置","x0",1,"[m]",0.11999999999999998,-80.419426705156098,2.2912595516279861,1.8959226900475026,15.792375061891766,-7.7517088731397538E-2,-0.15792375061891767,-64.627051643264338,2.2137424628965885,1.7379989394285849,null,-64.627063230507304,2.2137441070896409,1.7379991469000071,null,-1.1587242966015765E-5,1.6441930523747317E-6,2.0747142226440474E-7]
["初期速度","x'0",10,"[m/s]",0.13199999999999998,-79.370180228468598,1.3320866537616274,1.9176501730236333,15.771603760035847,0.11209437258057305,-0.15771603760035846,-63.598576468432753,1.4441810263422004,1.7599341354232747,null,-63.598589658409963,1.4441827194354311,1.7599343805180439,null,-1.3189977210004145E-5,1.6930932307257507E-6,2.4509476914680306E-7]
[null,null,null,null,0.14399999999999999,-77.894302876138369,0.38808202127486902,1.9279534708397155,15.523993766566027,0.30009361098862508,-0.15523993766566027,-62.370309109572339,0.6881756322634941,1.7727135331740551,null,-62.370323898581901,0.68817734827209964,1.7727138170988641,null,-1.4789009561866351E-5,1.7160086055456603E-6,2.8392480899697148E-7]
[null,"c/m",{"$f":"C12/C11","v":2},"[1/s]",0.156,-76.01030771759514,-0.53574389291065949,1.9270448875854111,15.053106388740833,0.48377668452758227,-0.15053106388740833,-60.95720132885431,-5.1967208383077224E-2,1.7765138236980027,null,-60.957217693762111,-5.1965495873850298E-2,1.776514147195237,null,-1.6364907800436868E-5,1.7125092269254516E-6,3.2349723433355848E-7]
[null,"k/m",{"$f":"C13/C11","v":40},"[1/s^2]",0.16800000000000001,-73.738590457046499,-1.43461424584911,1.9151954737186176,14.365714271771784,0.66050172945884522,-0.14365714271771785,-59.372876185274713,-0.77411251639026479,1.7715383310008999,null,-59.37289408445298,-0.77411083400305958,1.7715386943609965,null,-1.7899178267555271E-5,1.6823872052151856E-6,3.6336009667792268E-7]
[null,"μ'g",{"$f":"C15*C10","v":0},"[s^2/m]",0.18000000000000002,-71.101268763122079,-2.304007438694093,1.8927320910127563,13.471703989707493,0.82772695747872882,-0.13471703989707492,-57.629564773414586,-1.476280481215364,1.7580150511156813,null,-57.629584147780584,-1.4762788555709234,1.7580154541926094,null,-1.9374365997748555E-5,1.62564444061708E-6,4.0307692805718887E-7]
[null,"f/m",{"$f":"C16/C11","v":10},"[N/m]",0.19200000000000003,-68.122015612965001,-3.1396767857778065,1.860034229613015,12.383933849525381,0.98304721356901059,-0.1238393384952538,-55.738081763439624,-2.156629572208796,1.7361948911177612,null,-55.738102537575003,-2.156628029728525,1.7361953333471323,null,-2.0774135379042491E-5,1.5424802710661822E-6,4.4222937112259331E-7]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":6.324555320336759},"［rad/s］",0.20400000000000004,-64.825887740769048,-3.9376681533537443,1.8175306011869128,11.118048953596132,1.1242285686880584,-0.11118048953596131,-53.707838787172918,-2.8134395846656859,1.7063501116509514,null,-53.707860870504504,-2.8134381513864497,1.7063505920702797,null,-2.2083331586486565E-5,1.433279236184859E-6,4.8041932831921486E-7]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C27^2)","v":6.2449979983983983},"［rad/s］",0.21600000000000005,-61.239150282760477,-4.6943355158095539,1.7656955328594894,9.6922561804271794,1.2492404497652614,-9.6922561804271792E-2,-51.546894102333297,-3.4450950660442925,1.6687729710552177,null,-51.546917390357621,-3.4450937674450479,1.6687734883258636,null,-2.3288024323164791E-5,1.298599244581311E-6,5.1727064587225868E-7]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0.15811388300841897},"[ND]",0.22800000000000006,-57.389098706365225,-5.4063543902410807,1.7050451871711843,8.1270623200760923,1.3562848448817804,-8.1270623200760922E-2,-49.262036386289132,-4.0500695453593005,1.6237745639704233,null,-49.262060761823832,-4.05006840619905,1.6237751164007788,null,-2.4375534700027401E-5,1.1391602505739229E-6,5.5243035546048702E-7]
["減衰率","γ＝ζω",{"$f":"C27*C25","v":1},"[1/s]",0.24000000000000007,-53.303879100955903,-6.0707331232756054,1.6361336336876775,6.4449791305610251,1.4438221635874446,-6.4449791305610252E-2,-46.85889997039488,-4.6269109596881606,1.5716838423820672,null,-46.858925304842252,-4.6269100038544968,1.5716844279515687,null,-2.5334447371960778E-5,9.5583366377383072E-7,5.8556950155441712E-7]
["振幅","A1",{"$f":"SQRT(((C31*(C28*SIN(C32)+C17*COS(C32))-C28*C18-C19)/C26)^2+(C18-C31*SIN(C32))^2)","v":2.2673829938997163},"[m]",0.25200000000000006,-49.012307891344804,-6.6848220168692309,1.5595487981270812,4.6701995573617712,1.5105933804118765,-4.6701995573617712E-2,-44.342108333983035,-5.1742286364573546,1.5128468025534636,null,-44.34213448859186,-5.174227886824835,1.5128474189370584,null,-2.6154608825379455E-5,7.4963251961435162E-7,6.1638359483140448E-7]
["初期位相","β",{"$f":"ATAN2(C26*(C18-C31*SIN(C32)),C31*(C28*SIN(C32)+C17*COS(C32))-C28*C18-C19)","v":-1.0893191205886743},"[rad]",0.26400000000000007,-44.543692013307094,-7.2463202924118075,1.4759083149532675,2.8282497728583089,1.5556381430857469,-2.828249772858309E-2,-41.715442240448787,-5.6906821493260606,1.4476258172246843,null,-41.715469067563134,-5.6906816276234977,1.4476264618174151,null,-2.6827114346872349E-5,5.2170256292782824E-7,6.4459273074746193E-7]
["振幅","A2",{"$f":"C24/SQRT((C25^2-C17^2)^2+4*(C28*C17)^2)","v":0.158113883008419},"[m]",0.27600000000000008,-39.927650563145157,-7.7532809047856119,1.3858553093179093,0.94562204032915809,1.578308585026527,-9.4562204032915802E-3,-38.982028522816002,-6.1749723197590853,1.3763990889146178,null,-38.982055867100961,-6.1749720464448767,1.3763997588560313,null,-2.7344284958985554E-5,2.7331420859866284E-7,6.6994141345588787E-7]
["初期位相","α",{"$f":"ATAN2(C25^2-C17^2,-2*C28*C17)","v":-2.819842099193151},"[rad]",0.28800000000000009,-35.193938900919875,-8.2041132299789421,1.2900541340219438,-0.95060631707322674,1.5782786434275178,9.5060631707322672E-3,-36.144545217993098,-6.6258345865514245,1.299560197192676,null,-36.144572917629297,-6.6258345806960195,1.2995608893908106,null,-2.7699636198974531E-5,5.8554050497150456E-9,6.9219813458865076E-7]
[null,null,null,null,0.3000000000000001,-30.372276149785264,-8.5975836613927079,1.1891860868142667,-2.8331623621042339,1.5555487489306019,2.8331623621042339E-2,-33.205438511889497,-7.042034912462106,1.217517710435309,null,-33.205466399730646,-7.0420351916367334,1.2175184215900692,null,-2.7887841149265569E-5,-2.791746274155571E-7,7.1115476019123491E-7]
[null,null,null,null,0.31200000000000011,-25.492176992195169,-8.9328141610416765,1.0839451328569629,-4.6749698026732176,1.5104458194324404,4.6749698026732178E-2,-30.167146794868387,-7.4223683416092356,1.130694830883695,null,-30.167174699557133,-7.4223689217801301,1.1306955575094584,null,-2.7904688746360762E-5,-5.8017089443751502E-7,7.2662576333648587E-7]
["減衰振動項解析解",null,null,null,0.32400000000000012,-20.582788617944622,-9.2092788223903774,0.97503365656813423,-6.449538422795797,1.4436185581131908,6.4495384227957975E-2,-27.032327040740419,-7.7656602642771864,1.0395290407960922,null,-27.032354787780296,-7.7656611597046199,1.0395297792434608,null,-2.7747039876402368E-5,-8.9542743353376864E-7,7.3844736858674764E-7]
["x1''+2γx1'+ω^2x1=0",null,null,"運動方程式",0.33600000000000013,-15.672733629427849,-9.4267985115293182,0.86315826631216208,-8.1313450841727644,1.3560281233149241,8.1313450841727641E-2,-23.804078713600614,-8.0707703882143935,0.94447171715388967,null,-23.804106126382838,-8.0707716113559815,0.94447246363052462,null,-2.7412782223734666E-5,-1.223141588013732E-6,7.4647663494964434E-7]
["x1＝A1e^(－γt)cos(ωdt＋β)",null,null,"変位",0.34800000000000014,-10.78995965650585,-9.5855336627470731,0.7490256745499998,-9.696200818553411,1.2489343044623455,9.6962008185534104E-2,-20.486160475059261,-8.3365993582847278,0.84598768273553393,null,-20.486187375845311,-8.3366009197025814,0.84598843332607787,null,-2.6900786050276793E-5,-1.5614178536793588E-6,7.5059054394088776E-7]
["x1'＝－γx1－A1ωde^(－γt)sin(ωdt＋β)",null,null,"速度",0.36000000000000015,-5.9615963773658471,-9.6859753132491875,0.63333867509660546,-11.12159873109354,1.1238774028537928,0.1112159873109354,-17.083195108459385,-8.5620979103953943,0.74455466240754087,null,-17.083221319321098,-8.5620998186669528,0.74455541309266149,null,-2.6210861712172573E-5,-1.9082715585483356E-6,7.506851206207088E-7]
["x1''＝－2γx1'－ω^2x1",null,null,"加速度",0.37200000000000016,-1.2138205831099995,-9.7289344697821303,0.51679223806685637,-12.387037710908723,0.98265607792617482,0.12387037710908723,-13.600858294018723,-8.7462783918559559,0.64066261517594358,null,-13.600883637738963,-8.7462806534884248,0.64066336185057304,null,-2.5343720240655898E-5,-2.2616324688584655E-6,7.4667462945932073E-7]
["A1^2=[{(A2(γsinα+Ωcosα)-γx0-x0'}/ωd}^2+(x0-A2sinα)^2]",null,null,"振幅",0.38400000000000017,3.4282701370715181,-9.7155299072100227,0.40006974193371309,-13.474317292981837,0.82730147762499939,0.13474317292981836,-10.046047155910319,-8.8882284295850233,0.53481291486353144,null,-10.046071456848663,-8.8882310489335961,0.53481365335441866,null,-2.4300938344268275E-5,-2.6193485727077359E-6,7.384908872198892E-7]
["β=tan^(-1){(A2(γsinα+Ωcosα)-γx0-x0')/(ωd(x0-A2sinα))}",null,null,"初期位相",0.39600000000000019,7.9407745760065467,-9.6471745056394624,0.28383936088180939,-14.367799430506189,0.66004802495535209,0.1436779943050619,-6.427024854499642,-8.9871264806841111,0.42751735518687128,null,-6.4270479394275437,-8.9871294598743461,0.42751808126958057,null,-2.3084927901706465E-5,-2.9791902349529664E-6,7.2608270929030994E-7]
[null,null,null,null,0.4080000000000002,12.301095503947625,-9.5255602384737585,0.16875062432499729,-15.054633412663776,0.48330128088292418,0.15054633412663776,-2.7535379087161509,-9.0422589575908336,0.31929695845163508,null,-2.7535596076270483,-9.0422622964457595,0.31929766786715363,null,-2.1698910897427481E-5,-3.3388549258717148E-6,7.0941551855163709E-7]
["強制振動項解析解",null,null,null,0.42000000000000021,16.488037294495975,-9.3526419287872198,5.5431164076961595E-2,-15.524940692907329,0.2996033458042523,0.15524940692907327,0.96309660158864574,-9.0530385829829676,0.21068057100603488,null,0.96307645468843717,-9.0530422789556582,0.21068125947717461,null,-2.0146900208573015E-5,-3.6959726905649859E-6,6.8847113973702356E-7]
["x2''+2γx2'+ω^2x2=f/m",null,null,"運動方程式",0.43200000000000022,20.481893262097135,-9.1306198956330302,-5.5516336770776872E-2,-15.771956969411226,0.11159629720742356,0.15771956969411227,4.7099362926859083,-9.0190235984256066,0.1022032329233354,null,4.7099178589999848,-9.0190276465381878,0.10220389617111249,null,-1.8433685923469056E-5,-4.0481125811453467E-6,6.6324777708848259E-7]
["x2=A2sin(Ωt＋α)",null,null,"変位",0.44400000000000023,24.264522458254735,-8.8619216153290488,-0.16351698068991591,-15.792129474186746,-7.8015810610562675E-2,0.15792129474186747,8.472392984067989,-8.9399374259396112,-5.5956859480484344E-3,null,8.4723764192407369,-8.9399418187298014,-5.5950521878576796E-3,null,-1.6564827252096848E-5,-4.3927901902662825E-6,6.3376019075484652E-7]
["x2'=A2Ωcos(Ωt＋α)",null,null,"速度",0.45600000000000024,27.819415739570601,-8.5491825254040279,-0.26802626721906359,-15.58516807157873,-0.26650583822203616,0.15585168071578731,12.234247667991871,-8.8156883636260641,-0.11217458650327627,null,12.234233121342347,-8.8156930911025153,-0.11217398646321565,null,-1.4546649524049826E-5,-4.7274764511939793E-6,6.0004006062486237E-7]
["x2''=－A2Ω^2sin(Ωt＋α)",null,null,"加速度",0.46800000000000025,31.131750986181597,-8.1952261007360736,-0.36853246961773617,-15.154049431207874,-0.45116278477405913,0.15154049431207875,15.977701554973724,-8.6463888855101327,-0.21699197530565742,null,15.97768916872773,-8.6463939351179384,-0.21699141316911735,null,-1.2386245993312173E-5,-5.0496078056738725E-6,5.621365400665379E-7]
["A2=F/(m√((ω^2-Ω^2)^2+4(γΩ)^2))",null,null,"振幅",0.48000000000000026,34.188437413762138,-7.803043332483556,-0.46455876871987556,-14.504974215340363,-0.62933077957709405,0.14504974215340363,19.683463198421776,-8.4323741120606499,-0.31950902656647195,null,19.683453106938682,-8.4323794686585067,-0.31950850644950185,null,-1.0091483094498699E-5,-5.3565978568315131E-6,5.2011697010412306E-7]
["α=tan^(-1)((-2γΩ)/(ω^2-Ω^2))",null,null,"初期位相",0.49200000000000027,36.978148985653618,-7.3757717407090144,-0.55566513760588976,-13.647277896447266,-0.79844728077151061,0.13647277896447266,23.330871089206354,-8.1742190214805248,-0.41919235864141713,null,23.330863418197691,-8.1742246673310959,-0.4191918845736719,null,-7.6710086638343E-6,-5.6458505710565987E-6,4.7406774522640305E-7]
[null,null,null,null,0.50400000000000023,39.491346993531735,-6.9166740511451179,-0.64144997228103739,-12.593296487640501,-0.95607993167089089,0.12593296487640501,26.898050505891234,-7.8727539828160085,-0.51551700740463235,null,26.898045371629486,-7.8727598975910125,-0.51551658330933847,null,-5.1342617481964226E-6,-5.9147750040011715E-6,4.2409529388276468E-7]
["減衰振動＋強制振動　解析解",null,null,null,0.51600000000000024,41.720291935017748,-6.4291166653686176,-0.72155146510701273,-11.358189117148044,-1.0999615446873579,0.11358189117148043,30.362102817869705,-7.5290782100559754,-0.6079695739355323,null,30.36210032638677,-7.52908437085763,-0.60796920360837592,null,-2.4914829346300849E-6,-6.1608016546088606E-6,3.7032715638485314E-7]
["x=x1+x2",null,null,"変位",0.52800000000000025,43.659044874480593,-5.9165480517583138,-0.79564871927409897,-9.9597199986914386,-1.2280227096746457,9.9597199986914381E-2,33.699324875789152,-7.1445707614329592,-0.69605151928718456,null,33.699325122065524,-7.1445771428332225,-0.69605120637408058,null,2.4627637174035044E-7,-6.3814002633222344E-6,3.1291310398362526E-7]
["x'=x1'+x2'",null,null,"速度",0.54000000000000026,45.303458528687592,-5.3824771820428152,-0.86346260411504883,-8.418002933626612,-1.3384215576919474,8.4180029336266116E-2,36.885455595060982,-6.7208987397347624,-0.77928257477878271,null,36.885458662208066,-6.7209053138338479,-0.77928232275250553,null,3.067147083868349E-6,-6.5740990855545078E-6,2.5202627718101667E-7]
["x''=x1''+x2''",null,null,"加速度",0.55200000000000027,46.651158371682676,-4.8304521350249319,-0.92475635254082023,-6.7552120196038983,-1.4295702521044535,6.7552120196038984E-2,39.895946352078781,-6.2600223871293856,-0.85720423234478127,null,39.895952310517863,-6.2600291236348573,-0.85720404448048471,null,5.9584390825762057E-6,-6.7365054716717054E-6,1.8786429656358905E-7]
[null,null,null,null,0.56400000000000028,47.701514103067666,-4.2640389852352438,-0.97933590331492915,-4.9952627265465885,-1.500157826006232,4.9952627265465885E-2,42.706251376521081,-5.7641968112414759,-0.92938327604946325,null,42.706260283164504,-5.7642036775690819,-0.92938315539916849,null,8.9066434227902391E-6,-6.8663276060476619E-6,1.2065029475483158E-7]
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[null,"技術的なご質問のみお受けします。"]
[]
[null,null,"sxsijk@Gmail.com","sxsijk@Gmail.com"]
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[]
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