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{"sheet":"単振動","index":0,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,6]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,null,null,"単振動",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"ルンゲ･クッタ･ギル法\",\"ForcedOscillation\",C8:C18,J8:L8)","v":"ルンゲ･クッタ･ギル法"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,null,null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["ダンパ＋バネ＋動摩擦＋外力",null,null,null,null,null,"解析解",null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,null,null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-($C$25^2)*H8","v":-100},{"$f":"-$C$31*$C$25*SIN($C$25*E8+$C$32)","v":0},{"$f":"$C$31*COS($C$25*E8+$C$32)","v":1},null,-100,0,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-99.280863585386626,-1.1971220728891936,0.99280863585386625,null,-99.280863999999994,-1.1971200000000009,0.99280863999999991,null,{"$f":"J9-F9","v":-4.1461336763859435E-7},{"$f":"K9-G9","v":2.0728891927390691E-6},{"$f":"L9-H9","v":4.1461336586223752E-9}]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-97.133797485202962,-2.377026264271346,0.97133797485202966,null,-97.133803271464956,-2.3770221582336015,0.97133803271464958,null,-5.7862619939896831E-6,4.1060377444779306E-6,5.7862619917692371E-8]
["質量","m",10,"[kg]",3.6000000000000004E-2,-93.589682367793486,-3.5227423327508998,0.93589682367793481,null,-93.589698357906073,-3.5227363218891288,0.9358969835790607,null,-1.5990112586905525E-5,6.0108617709886403E-6,1.599011258957006E-7]
["粘性係数","c",0,"[Ns/m]",4.8000000000000001E-2,-88.699492277928414,-4.6177917554148289,0.88699492277928416,null,-88.699523039063038,-4.6177840537955133,0.88699523039063044,null,-3.0761134624412989E-5,7.7016193156254076E-6,3.0761134628409792E-7]
["バネ定数","k",1000,"[N/m]",0.06,-82.533561490967827,-5.6464247339503535,0.82533561490967833,null,-82.533611190581141,-5.6464156364676423,0.82533611190581146,null,{"$f":"J13-F13","v":-4.9699613313691771E-5},{"$f":"K13-G13","v":9.0974827111622858E-6},{"$f":"L13-H13","v":4.9699613313691771E-7}]
["動摩擦係数","μ'",0,"[ND]",7.1999999999999995E-2,-75.18057291408951,-6.5938467197147315,0.75180572914089505,null,-75.180645193681499,-6.5938365952008606,0.75180645193681506,null,{"$f":"J14-F14","v":-7.2279591989854453E-5},{"$f":"K14-G14","v":1.0124513870835017E-5},{"$f":"L14-H14","v":7.2279592000512594E-7}]
["強制力","f",0,"[N]",8.3999999999999991E-2,-66.746282584130824,-7.4464311997085915,0.66746282584130823,null,-66.746380444214608,-7.4464204822061975,0.66746380444214615,null,-9.7860083783984919E-5,1.0717502394008704E-5,9.7860083791978525E-7]
["強制力角速度","Ω",0,"[rad/s]",9.5999999999999988E-2,-57.351998607245683,-8.1919156830099809,0.5735199860724568,null,-57.352124306084619,-8.1919048613810599,0.57352124306084618,null,-1.2569883893576161E-4,1.0821628920965054E-5,1.2569883893753797E-6]
["初期位置","x0",1,"[m]",0.10799999999999998,-47.132836417374016,-8.8195780688494736,0.47132836417374013,null,-47.132991385778304,-8.8195676749301199,0.47132991385778306,null,-1.5496840428852465E-4,1.0393919353646197E-5,1.5496840429229941E-6]
["初期速度","x'0",0,"[m/s]",0.11999999999999998,-36.235775447667386,-9.320390859672262,0.36235775447667384,null,-36.235960221833921,-9.3203814552127646,0.36235960221833918,null,-1.8477416653439604E-4,9.4044594973752282E-6,1.8477416653395196E-6]
[null,null,null,null,0.13199999999999998,-24.817545165237313,-9.6871510011826523,0.24817545165237312,null,-24.817759339268719,-9.6871431638386252,0.24817759339268719,null,-2.1417403140588931E-4,7.8373440270951278E-6,2.1417403140711055E-6]
[null,"c/m",{"$f":"C12/C11","v":0},"[1/s]",0.14399999999999999,-13.042370873814555,-9.9145834819168641,0.13042370873814554,null,-13.042613073172172,-9.9145777905781767,0.13042613073172171,null,-2.4219935761671252E-4,5.6913386874413163E-6,2.4219935761682354E-6]
[null,"k/m",{"$f":"C13/C11","v":100},"[1/s^2]",0.156,-1.0796117058267392,-9.9994172022996626,1.0796117058267392E-2,null,-1.0798795825653298,-9.9994142220596842,1.0798795825653297E-2,null,-2.6787673859063332E-4,2.9802399783562805E-6,2.67876738590557E-6]
[null,"μ'g",{"$f":"C14*C10","v":0},"[s^2/m]",0.16800000000000001,10.898675223987134,-9.9404320219807598,-0.10898675223987134,null,10.898384973781647,-9.9404322890585401,-0.10898384973781647,null,-2.9025020548623104E-4,-2.6707778033596696E-7,2.9025020548689717E-6]
[null,"f/m",{"$f":"C15/C11","v":0},"[N/m]",0.18000000000000002,22.720209469308731,-9.7384763087819515,-0.2272020946930873,null,22.719901065894359,-9.7384803157141633,-0.2271990106589436,null,-3.0840341437254892E-4,-4.0069322118085893E-6,3.0840341437021745E-6]
["振動中心","p＝mg/k",{"$f":"C11*C10/C13","v":9.8000000000000004E-2},"[m]",0.19200000000000003,34.214965115089853,-9.3964547368532472,-0.34214965115089857,null,34.214643633712875,-9.396462918270915,-0.34214643633712877,null,-3.2148137697873835E-4,-8.1814176677852402E-6,3.2148137698029267E-6]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":10},"［rad/s］",0.20400000000000004,45.217616214091237,-8.9192865095337943,-0.45217616214091239,null,45.217287502791628,-8.9192992288310737,-0.45217287502791625,null,-3.2871129960909684E-4,-1.2719297279417674E-5,3.2871129961309364E-6]
["〝","〝",{"$f":"DEGREES(C25)","v":572.95779513082323},"[deg/s]",0.21600000000000005,55.569914625061315,-8.3138346077868288,-0.55569914625061312,null,55.569585202953817,-8.3138521449754066,-0.5556958520295382,null,-3.2942210749808964E-4,-1.7537188577776419E-5,3.2942210749231648E-6]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C29^2)","v":10},"［rad/s］",0.22800000000000006,65.122966052754634,-7.5888070818092146,-0.65122966052754627,null,65.12264299050166,-7.5888296228325149,-0.65122642990501667,null,-3.2306225297418223E-4,-2.2541023300348684E-5,3.2306225296041546E-6]
["〝","〝",{"$f":"DEGREES(C27)","v":572.95779513082323},"[deg/s]",0.24000000000000007,73.739371554124602,-6.7546318055115027,-0.737393715541246,null,73.739062338690758,-6.7546594332681682,-0.73739062338690753,null,-3.0921543384465622E-4,-2.7627756665538072E-5,3.0921543384687666E-6]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0},"[ND]",0.25200000000000006,81.295203709989025,-5.8233064952408151,-0.81295203709989028,null,81.294916096104771,-5.8233391825372056,-0.81294916096104775,null,-2.8761388425380119E-4,-3.2687296390498943E-5,2.876138842533571E-6]
["減衰率","γ＝ζω",{"$f":"C29*C25","v":0},null,0.26400000000000007,87.681789039428168,-4.8082261498864787,-0.87681789039428171,null,87.68153089048684,-4.808263754503785,-0.87681530890486836,null,-2.5814894132736299E-4,-3.7604617306286059E-5,2.5814894133446842E-6]
["振幅","A",{"$f":"SQRT($C$17^2+($C$18/$C$25)^2)","v":1},"[m]",0.27600000000000008,92.807271020933285,-3.7239903942505488,-0.92807271020933291,null,92.807050142293804,-3.7240326562739994,-0.92807050142293801,null,-2.2087863948172526E-4,-4.2262023450589936E-5,2.2087863948971886E-6]
["初期位相","α",{"$f":"ATAN2($C$17,-$C$18/$C$25)","v":0},"[rad]",0.28800000000000009,96.597931239797504,-2.5861934966110995,-0.96597931239797497,null,96.597755207661265,-2.5862400381275479,-0.96597755207661262,null,-1.7603213623829106E-4,-4.6541516448339593E-5,1.7603213623429426E-6]
["〝","〝",{"$f":"DEGREES(C32)","v":0},"[deg]",0.3000000000000001,98.999249660044569,-1.4112000805986635,-0.98999249660044564,null,98.999125649214349,-1.4112504078250037,-0.98999125649214348,null,-1.2401083021984505E-4,-5.0327226340129982E-5,1.2401083021584824E-6]
["A^2＝x0^2＋(x'0/ω)^2",null,null,null,0.31200000000000011,99.976688771292842,-0.21590975726095071,-0.99976688771292843,null,99.976623385201094,-0.21596326512031153,-0.99976623385201091,null,-6.538609174810972E-5,-5.3507859360812926E-5,6.5386091752106523E-7]
["α＝atan2(x0,－x'0/ω)",null,null,null,0.32400000000000012,99.516190332383019,0.98248593745109569,-0.99516190332383025,null,99.516189438794527,0.98242995833486413,-0.99516189438794522,null,-8.9358849209020264E-7,-5.5979116231563708E-5,8.9358850319243288E-9]
[null,null,null,null,0.33600000000000013,97.624377567240955,2.1667508038738093,-0.97624377567240961,null,97.624446142990124,2.1666931578393909,-0.97624446142990129,null,6.8575749168076072E-5,-5.7646034418379344E-5,-6.8575749168076072E-7]
["単振動解析解",null,null,null,0.34800000000000014,94.328459904847534,3.3198518822073537,-0.94328459904847539,null,94.328601892862594,3.3197934569987955,-0.94328601892862596,null,1.4198801505926895E-4,-5.8425208558254837E-5,-1.4198801505660441E-6]
["x''+ω^2x=0",null,"運動方程式",null,0.36000000000000015,89.675841633414635,4.4252044329485365,-0.89675841633414632,null,89.676059815111941,4.4251461861037091,-0.89676059815111941,null,2.1818169730636328E-4,-5.8246844827358757E-5,-2.1818169730902781E-6]
["x＝Acos{ωt＋α}",null,"解析解",null,0.37200000000000016,83.733440097387927,5.4669104706928824,-0.83733440097387923,null,83.733735983291467,5.4668534140854792,-0.83733735983291468,null,2.9588590354023836E-4,-5.7056607403183079E-5,-2.9588590354512334E-6]
["x'＝－Aωsin{ωt＋α}",null,null,null,0.38400000000000017,76.586723243463624,6.4299874205391019,-0.76586723243463628,null,76.587096984620644,6.42993260332074,-0.76587096984620651,null,3.737411570199356E-4,-5.4817218361868925E-5,-3.7374115702260013E-6]
["x''＝－ω^2x",null,null,null,0.39600000000000019,68.338480358333499,7.3005836083930076,-0.68338480358333498,null,68.338930680762004,7.3005320986168147,-0.68338930680762,null,4.5032242850595594E-4,-5.1509776192837364E-5,-4.5032242850240323E-6]
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{"sheet":"単振動＋外力","index":1,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,6]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,null,null,"単振動",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"ルンゲ･クッタ･ギル法\",\"ForcedOscillation\",C8:C18,J8:L8)","v":"ルンゲ･クッタ･ギル法"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,null,null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["ダンパ＋バネ＋動摩擦＋外力",null,null,null,null,null,"解析解",null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,null,null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-($C$25^2)*H8-$C$34*$C$16^2*SIN($C$16*E8+$C$35)","v":-100},{"$f":"-$C$31*$C$25*SIN($C$25*E8+$C$32)+$C$34*$C$16*COS($C$16*E8+$C$35)","v":2400},{"$f":"$C$31*COS($C$25*E8+$C$32)+$C$34*SIN($C$16*E8+$C$35)","v":1},null,-100,0,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":-2400},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-28281.219525592584,2244.9552547541543,29.17474729786106,null,-95.76671508677353,-1.1757779297190065,0.99289457419524429,null,{"$f":"J9-F9","v":28185.452810505809},-2246.1310326838734,-28.181852723665816]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-52847.907555203055,1801.9567236738769,53.722111732569878,null,-90.607139864780208,-2.2946971456421634,0.97200986584494942,null,52757.300415338272,-1804.2514208195191,-52.750101866724933]
["質量","m",10,"[kg]",3.6000000000000004E-2,-70650.214233163599,1127.6653316842251,71.492521374473739,null,-84.988741334723841,-3.3485223510976083,0.93808319403573304,null,70565.225491828882,-1131.0138540353228,-70.554438180438012]
["粘性係数","c",0,"[Ns/m]",4.8000000000000001E-2,-79405.367347612846,308.39910921613449,80.203662778114193,null,-79.277334571491437,-4.334068627151483,0.89191918053408303,null,79326.09001304135,-312.733177843286,-79.311743597580104]
["バネ定数","k",1000,"[N/m]",0.06,-77990.344031746601,-550.93145199735886,78.733146085165302,null,-73.695281563920091,-5.2517123654560525,0.83433757872702052,null,{"$f":"J13-F13","v":77916.648750182678},{"$f":"K13-G13","v":545.67973963190286},{"$f":"L13-H13","v":-77.898808506438286}]
["動摩擦係数","μ'",0,"[ND]",7.1999999999999995E-2,-66585.85743520876,-1340.2717977211844,67.262482591435571,null,-68.300316393524326,-6.1035203003340222,0.76614151001311159,null,{"$f":"J14-F14","v":66517.557118815239},1334.1682774208505,-66.496341081422457]
["強制力","f",100,"[N]",8.3999999999999991E-2,-46653.198244510706,-1958.5313202394439,47.253914787767883,null,-62.987606024784675,-6.8912627255508783,0.68810912520025491,null,46590.210638485922,1951.640057513893,-46.565805662567627]
["強制力角速度","Ω",30,"[rad/s]",9.5999999999999988E-2,-20746.899971496143,-2326.5422654381491,21.263067958961354,null,-57.514646402014591,-7.6145903783104654,0.60100839898625691,null,20689.385325094128,2318.9276750598387,-20.662059559975098]
["初期位置","x0",1,"[m]",0.10799999999999998,7812.7546631912501,-2397.2081460460422,-7.3885591354348845,null,-51.545637249344907,-8.2696316824789893,0.50563151311893817,null,-7864.3003004405946,2388.9385143635632,7.8941906485538222]
["初期速度","x'0",0,"[m/s]",0.11999999999999998,35365.399688140496,-2161.5405900616256,-35.039277709111488,null,-44.709455379547897,-8.8482110127844429,0.40284250946599365,null,-35410.109143520043,2152.6923790488413,35.442120218577479]
[null,null,null,null,0.13199999999999998,58379.851321978706,-1649.8106796011903,-58.156493415491575,null,-36.663579352864964,-9.337806585930716,0.29362995744471959,null,-58416.514901331568,1640.4728730152594,58.450123372936297]
[null,"c/m",{"$f":"C12/C11","v":0},"[1/s]",0.14399999999999999,73906.810326981198,-927.66718599235151,-73.789428989116857,null,-27.155534863489315,-9.7222690583343319,0.17915553276257432,null,-73933.965861844685,917.94491693401721,73.968584521879436]
[null,"k/m",{"$f":"C13/C11","v":100},"[1/s^2]",0.156,79956.962214476895,-87.719379825639024,-79.947245709124459,null,-16.073731008191952,-9.9832214558721386,6.0789757799191123E-2,null,-79973.035945485084,77.736158369766883,80.008035466923644]
[null,"μ'g",{"$f":"C14*C10","v":0},"[s^2/m]",0.16800000000000001,75756.0007226327,762.33643817735162,-75.854088799648594,null,-3.4809042929460414,-10.101970599598912,-5.9872334629800412E-2,null,-75759.481626925641,-772.4384087769505,75.794216465018792]
[null,"f/m",{"$f":"C15/C11","v":10},"[N/m]",0.18000000000000002,61843.879213948276,1513.5244259535414,-62.048361099172062,null,10.374392602852307,-10.061691365319644,-0.18102037478412167,null,-61833.504821345421,-1523.5861173188609,61.867340724387944]
["振動中心","p＝mg/k",{"$f":"C11*C10/C13","v":9.8000000000000004E-2},"[m]",0.19200000000000003,40005.565614467218,2069.5604987712954,-40.31350030050303,null,25.070011159371788,-9.8496067948521091,-0.30066429990540788,null,-39980.495603307849,-2079.4101055661476,40.012836000597623]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":10},"［rad/s］",0.20400000000000004,13042.178833426355,2359.1962299310076,-13.449137379353175,null,40.044852280007973,-9.4588842237176536,-0.41669472432159488,null,-13002.133981146346,-2368.6551141547252,13.032442655031581]
["〝","〝",{"$f":"DEGREES(C25)","v":572.95779513082323},"[deg/s]",0.21600000000000005,-15588.15129341855,2345.3527917623342,15.088022061792998,null,54.651774872215903,-8.8900006183217322,-0.52696309721210433,null,15642.803068290767,-2354.2427923806558,-15.614985159005101]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C29^2)","v":10},"［rad/s］",0.22800000000000006,-42213.656229381828,2029.8739157107623,41.62754953490704,null,68.222258201317388,-8.1513950396056387,-0.6293741080188805,null,42281.878487583148,-2038.0253107503679,-42.256923642925919]
["〝","〝",{"$f":"DEGREES(C27)","v":572.95779513082323},"[deg/s]",0.24000000000000007,-63419.689736378219,1453.288523071896,62.756035392391091,null,80.134791171178179,-7.2593143194975172,-0.7219811253268662,null,63499.824527549397,-1460.5478373913934,-63.478016517717954]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0},"[ND]",0.25200000000000006,-76486.522853923409,689.61347287714295,75.754866020533512,null,89.878469689754837,-6.2368583937862931,-0.80307492432550664,null,76576.401323613158,-695.85033127092925,-76.557940944859013]
["減衰率","γ＝ζω",{"$f":"C29*C25","v":0},null,0.26400000000000007,-79738.0445352065,-163.13723526044242,78.948908433851656,null,97.103879868578261,-5.1123314581127204,-0.87125664078047527,null,79835.148415075077,158.0249038023297,-79.820165074632129]
["振幅","A",{"$f":"SQRT($C$17^2+($C$18/$C$25)^2)","v":1},"[m]",0.27600000000000008,-72756.662100637375,-995.5200032119244,71.921396661448981,null,101.654953751983,-3.9170914589955461,-0.92548770080525711,null,72858.317054389365,991.60291175292889,-72.846884362254244]
["初期位相","α",{"$f":"ATAN2($C$17,-$C$18/$C$25)","v":0},"[rad]",0.28800000000000009,-56436.849727630339,-1700.6946606510539,55.567468346472161,null,103.5778996004498,-2.6831523673340119,-0.96511218643091035,null,56540.427627230791,1698.0115082837199,-56.532580532903069]
["〝","〝",{"$f":"DEGREES(C32)","v":0},"[deg]",0.3000000000000001,-32870.479569680218,-2188.123828603827,31.97948632273982,null,103.10622114915974,-1.440823301369726,-0.98985036296742224,null,32973.585790829376,2186.6830053024573,-32.969336685707241]
["強制振動振幅","B",{"$f":"(1/$C$11)*($C$16^2-$C$25^2)","v":80},"[m]",0.31200000000000011,-5078.6366630336952,-2395.1822492654505,4.17884646409206,null,100.62387672532917,-0.21666210208651993,-0.99976550056353564,null,5179.2605397590241,2394.965587163364,-5.1786119646555955]
["初期位相","β",0,"[rad]",0.32400000000000012,23375.699435651921,-2295.1876654618904,-24.271345148643366,null,96.611400760614515,0.96802072977617637,-0.99520923666279471,null,-23279.088034891305,2296.1556861916665,23.276135911980571]
["〝","〝",{"$f":"DEGREES(C35)","v":0},"[deg]",0.33600000000000013,48844.44966265234,-1900.8236123253905,-49.723069060757503,null,91.581962179594342,2.0979433842785764,-0.97675315340229985,null,-48752.867700472743,1902.9215557096691,48.746315907355203]
["A^2＝x0^2＋(x'0/ω)^2",null,null,null,0.34800000000000014,68062.143111974161,-1262.5152694032452,-68.911099251117804,null,86.015590954841826,3.1638472639015296,-0.94511567786350503,null,-67976.127521019313,1265.6791166671467,67.965983573254306]
["α＝atan2(x0,－x'0/ω)",null,null,null,0.36000000000000015,78564.574246952805,-461.96657105984667,-79.371656821653531,null,80.300005142054161,4.1617336362957209,-0.9010936744271909,null,-78484.274241810752,466.12830469614238,78.470563147226343]
["B＝(1/m)/(Ω^2－ω^2)",null,null,null,0.37200000000000016,79004.735100002159,398.31286920971019,-79.758336060878634,null,74.685590659242379,5.0914683355014692,-0.84550715866730475,null,-78930.04950934292,-393.22140087420871,78.912828902211331]
["β＝0",null,null,null,0.38400000000000017,69325.517867895891,1208.1483328704489,-70.014798377087061,null,69.260238266552875,5.9549608394042988,-0.77916354659634424,null,-69256.257629629341,-1202.1933720310446,69.23563483049071]
[null,null,null,null,0.39600000000000019,50767.046223197918,1863.8233897935268,-51.382092546422925,null,63.947164017992577,6.7541776144004064,-0.70284502485847511,null,-50703.099059179927,-1857.0692121791265,50.679247521564449]
["単振動解析解",null,null,null,0.4080000000000002,25707.695281224962,2281.3754268245452,-26.239661374329689,null,58.5258618984113,7.4892694815444099,-0.61731935390604609,null,-25649.16941932655,-2273.8861573430008,25.622342020423641]
["x''+ω^2x=0",null,"運動方程式",null,0.42000000000000021,-2640.8176955574336,2407.3587629265467,2.1995829563508056,null,52.673342615264602,8.1570763951540037,-0.52337112143053144,null,2693.4910381726982,-2399.2016865313926,-2.722954077781337]
["x＝Acos{ωt＋α}",null,"解析解",null,0.43200000000000022,-30645.180741237924,2225.6954716609835,30.301023515296514,null,46.02018494794784,8.7502225579292059,-0.42184757393821676,null,30691.200926185873,-2216.9452491030543,-30.722871089234729]
["x'＝－Aωsin{ωt＋α}",null,null,null,0.44400000000000023,-54716.284357652767,1759.7356100704096,54.474154564847112,null,38.214002923383752,9.2569367262065008,-0.31371104464888178,null,54754.498360576152,-1750.4786733442031,-54.787865609495995]
["x''＝－ω^2x",null,null,null,0.45600000000000024,-71769.350494047016,1069.2627348271494,71.632730621398508,null,28.981960289262151,9.6616369284470682,-0.20008893979275036,null,71798.332454336283,-1059.6010978987024,-71.832819561191258]
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["強制振動成分",null,null,null,0.48000000000000026,-77261.372022285999,-613.60000882467205,77.340121107381492,null,5.8501694717567325,10.091886585149325,3.8064082937360195E-2,null,77267.222191757755,623.69189540982143,-77.302057024444139]
["x2＝Bsin(Ωt＋β)",null,null,null,0.49200000000000027,-64998.939151501327,-1390.2273577171109,65.184449680981885,null,-7.8044057886771689,10.081316799040581,0.15926696647483149,null,64991.134745712647,1400.3086745161515,-65.025182714507054]
["x2'＝BΩcos(Ωt＋β)",null,null,null,0.50400000000000023,{"$f":"-($C$25^2)*H50-$C$34*$C$16^2*SIN($C$16*E50+$C$35)","v":-44405.575530900751},{"$f":"-$C$31*$C$25*SIN($C$25*E50+$C$32)+$C$34*$C$16*COS($C$16*E50+$C$35)","v":-1987.5049338242175},{"$f":"$C$31*COS($C$25*E50+$C$32)+$C$34*SIN($C$16*E50+$C$35)","v":44.695179357225506},null,-22.386800897215124,9.9008514154355023,0.27933475563212068,null,44383.188730003538,1997.4057852396529,-44.415844601593385]
["x2''＝－BΩ^2sin(Ωt＋β)",null,null,null,0.51600000000000024,-18122.797674101799,-2328.8940537482699,18.512329504124306,null,-37.357471229314683,9.5424690774529068,0.39617410774271505,null,18085.440202872483,2338.4365228257229,-18.11615539638159]
[null,null,null,null,0.52800000000000025,10478.511536124086,-2370.6780599764929,-9.9946542328762238,null,-52.080228158751581,9.0052607531278994,0.50763693976413149,null,-10530.591764282837,2379.6833207296208,10.502291172640355]
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[null,null,null,null,5.9519999999999325,-39010.16061333126,-2095.3652315425848,38.123174005537784,null,103.41519460755038,-1.7378125231067503,-0.98526605272460988,null,39113.575807938811,2093.6274190194781,-39.108440058262396]
[null,null,null,null,5.963999999999932,-11916.971779902389,-2373.2720573167117,11.01810828996366,null,101.37326088523234,-0.50718680250590509,-0.99871155197627859,null,12018.345040787621,2372.7648705142055,-12.016819841939938]
[null,null,null,null,5.9759999999999316,16715.416528904268,-2346.9675129370053,-17.61322879164063,null,97.680962005396708,0.68853383948740021,-0.99757919456770916,null,-16617.735566898871,2347.6560467764925,16.61564959707292]
[null,null,null,null,5.9879999999999312,43216.136945583123,-2019.6875081598009,-44.0999849912847,null,92.849706371300329,1.832598246845542,-0.98239447822215475,null,{"$f":"J507-F507","v":-43123.287239211822},{"$f":"K507-G507","v":2021.5201064066464},{"$f":"L507-H507","v":43.117590513062545}]
[null,null,null,null,5.9999999999999307,64187.452156648636,-1433.2560595318332,-65.044623839022478,null,87.373186240241793,2.9143512478426814,-0.95384712597581112,null,{"$f":"J508-F508","v":-64100.078970408395},1436.1704107796759,64.090776713046665]

{"sheet":"減衰振動","index":2,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,6]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,null,null,"単振動",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"ルンゲ･クッタ･ギル法\",\"ForcedOscillation\",C8:C18,J8:L8)","v":"ルンゲ･クッタ･ギル法"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,null,null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["ダンパ＋バネ＋動摩擦＋外力",null,null,null,null,null,"解析解",null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,null,null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-2*$C$30*G8-$C$25^2*H8","v":-100},{"$f":"-$C$30*H8-$C$31*$C$27*EXP(-$C$30*E8)*SIN($C$27*E8+$C$32)","v":0},{"$f":"$C$31*EXP(-$C$30*E8)*COS($C$27*E8+$C$32)","v":1},null,-100,0,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-96.920839204435737,-1.1828708727782158,0.99286580949992165,null,-96.920851302399996,-1.182869068800001,0.99286589439999995,null,{"$f":"J9-F9","v":-1.2097964258828142E-5},1.8039782148093764E-6,8.4900078300975679E-8]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-92.537307219253776,-2.3208804232363018,0.97179068065726382,null,-92.537334937895537,-2.3208771272259408,0.97179089192347412,null,-2.7718641760543505E-5,3.296010361086843E-6,2.1126621030376214E-7]
["質量","m",10,"[kg]",3.6000000000000004E-2,-86.942632882240261,-3.3989196737188783,0.93740472229678018,null,-86.942679028080605,-3.3989152567879088,0.93740509541656425,null,-4.6145840343569944E-5,4.4169309694197523E-6,3.7311978406950885E-7]
["粘性係数","c",20,"[Ns/m]",4.8000000000000001E-2,-80.24504633494405,-4.4030902136626189,0.89051226762269298,null,-80.245112934402073,-4.4030850942297635,0.89051283122861602,null,-6.6599458023119951E-5,5.1194328554160506E-6,5.6360592304294244E-7]
["バネ定数","k",1000,"[N/m]",0.06,-72.565885163859775,-5.3208730092327556,0.83207631182325281,null,-72.565973419336061,-5.320867640326413,0.8320770869998888,null,{"$f":"J13-F13","v":-8.825547628532604E-5},{"$f":"K13-G13","v":5.3689063426176631E-6},{"$f":"L13-H13","v":7.7517663599202535E-7}]
["動摩擦係数","μ'",0,"[ND]",7.1999999999999995E-2,-64.037559176566816,-6.1412736067351483,0.76320106390037112,null,-64.037669442972842,-6.1412684627476581,0.76320206368468158,null,{"$f":"J14-F14","v":-1.1026640602551652E-4},5.1439874901859639E-6,9.9978431045144589E-7]
["強制力","f",0,"[N]",8.3999999999999991E-2,-54.80140608879708,-6.8549422260493182,0.68511290540895708,null,-54.801537870565014,-6.8549377892377823,0.68511413449040581,null,-1.3178176793360308E-4,4.4368115359461058E-6,1.229081448728131E-6]
["強制力角速度","Ω",0,"[rad/s]",9.5999999999999988E-2,-45.00547118332166,-7.4542676328389419,0.59914006448999546,null,-45.005623151521107,-7.4542643798655615,0.59914151911252234,null,-1.519681994466282E-4,3.2529733804409489E-6,1.4546225268752266E-6]
["初期位置","x0",1,"[m]",0.10799999999999998,-34.802244298007238,-7.9334440772918065,0.50669132452590848,null,-34.802414326803692,-7.9334424660893168,0.50669299258982325,null,-1.7002879645389157E-4,1.6112024896486332E-6,1.6680639147725884E-6]
["初期速度","x'0",0,"[m/s]",0.11999999999999998,-24.346387315763192,-8.2885109867969309,0.40923409289357054,null,-24.346572537085098,-8.2885114440320944,0.40923595425149289,null,-1.8522132190668117E-4,-4.5723516350903992E-7,1.8613579223503152E-6]
[null,null,null,null,0.13199999999999998,-13.792484677415661,-8.5173654945870645,0.30827215666589791,null,-13.792681552358811,-8.5173684039776951,0.30827418360314202,null,-1.9687494314979403E-4,-2.9093906306343342E-6,2.0269372441039657E-6]
[null,"c/m",{"$f":"C12/C11","v":2},"[1/s]",0.14399999999999999,-3.2928483401412016,-8.619748270471435,0.20532344881084072,null,-3.2930527453356007,-8.6197539621905506,0.20532560669716701,null,-2.044051943990155E-4,-5.691719115574756E-6,2.1578863262927683E-6]
[null,"k/m",{"$f":"C13/C11","v":100},"[1/s^2]",0.156,7.0045929148268744,-8.5972034881474606,0.10189814061468047,null,7.0043855879251407,-8.5972122295221105,0.1019003887111908,null,-2.073269017337509E-4,-8.7413746499009903E-6,2.2480965103238715E-6]
[null,"μ'g",{"$f":"C14*C10","v":0},"[s^2/m]",0.16800000000000001,16.958291829381583,-8.4530141113489048,-5.2263606683773829E-4,null,16.958086564530461,-8.4530260990320372,-5.2034366466386533E-4,null,-2.0526485112171144E-4,-1.1987683132375082E-5,2.2924021738729644E-6]
[null,"f/m",{"$f":"C15/C11","v":0},"[N/m]",0.18000000000000002,26.434942935271746,-8.192114003808209,-0.10050714927655328,null,26.434744973244968,-8.1921293575698257,-0.10050486258105315,null,-1.9796202677824226E-4,-1.5353761616765382E-5,2.2866955001338285E-6]
["振動中心","p＝mg/k",{"$f":"C11*C10/C13","v":9.8000000000000004E-2},"[m]",0.19200000000000003,35.311181577662339,-7.8209786616898089,-0.19669224254282716,null,35.310996292365189,-7.8209974199393848,-0.19669001452486415,null,-1.8528529714956221E-4,-1.875824957586758E-5,2.2280179630129737E-6]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":10},"［rad/s］",0.20400000000000004,43.475101373605277,-7.3474966283042713,-0.28780108116996733,null,43.474934145130149,-7.3475187454207074,-0.28779896654288734,null,-1.6722847512795624E-4,-2.2117116436071171E-5,2.114627079996545E-6]
["〝","〝",{"$f":"DEGREES(C25)","v":572.95779513082323},"[deg/s]",0.21600000000000005,50.827572845734679,-6.7808238766000875,-0.37265925092534502,null,50.827428933004256,-6.7808492221089818,-0.37265730488786292,null,-1.4391273042235753E-4,-2.5345508894325519E-5,1.9460374821034243E-6]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C29^2)","v":9.9498743710661994},"［rad/s］",0.22800000000000006,57.283349206401283,-6.1312236327846152,-0.45020901940832053,null,57.283233622019353,-6.1312519923859679,-0.45020729637247414,null,-1.1558438193048914E-4,-2.8359601352612174E-5,1.7230358463904416E-6]
["〝","〝",{"$f":"DEGREES(C27)","v":570.08580814747756},"[deg/s]",0.24000000000000007,62.771948624961965,-5.4098942626753956,-0.51952160099611178,null,62.771866014815508,-5.4099253410887664,-0.5195201533263798,null,-8.2610146456829625E-5,-3.1078413370799751E-5,1.4476697319798504E-6]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0.1},"[ND]",0.25200000000000006,67.238305740419079,-4.62878794986021,-0.57980729840698664,null,67.238260270452301,-4.6288213754194905,-0.5798061751961332,null,-4.5469966778455273E-5,-3.3425559280431116E-5,1.123210853437584E-6]
["減衰率","γ＝ζω",{"$f":"C29*C25","v":1},null,0.26400000000000007,70.643188632614908,-3.8004229608884588,-0.63042342710837995,null,70.643183885029771,-3.8004582917852905,-0.63042267301459187,null,-4.7475851374656486E-6,-3.5330896831720082E-5,7.540937880801124E-7]
["振幅","A＝x0",{"$f":"SQRT(($C$17^2+2*$C$17*$C$29*($C$18/$C$25)+($C$18/$C$25)^2)/(1-$C$29^2))","v":1.0050378152592121},"[m]",0.27600000000000008,72.963380888175436,-2.9376923175676324,-0.67087996253040172,null,72.963419769108,-2.9377290496117747,-0.67087961669884444,null,3.8880932564211435E-5,-3.6732044142340214E-5,3.4583155728018511E-7]
["初期位相","α＝0",{"$f":"ATAN2($C$17,-($C$18+$C$29*$C$25*$C$17)/($C$25*SQRT(1-$C$29^2)))","v":-0.1001674211615598},"[rad]",0.28800000000000009,74.191631744383599,-2.053671680623034,-0.70084288383137527,null,74.191716404864081,-2.0537092563601731,-0.70084297892143732,null,8.466048048205721E-5,-3.757573713913942E-5,-9.509006204666548E-8]
["〝","〝",{"$f":"DEGREES(C32)","v":-5.7391704772667866},"[deg]",0.3000000000000001,74.336380519379588,-1.1614291936856629,-0.72013522132008267,null,74.336512291113308,-1.1614670126886493,-0.72013578265736022,null,1.3177173372014295E-4,-3.781900298638341E-5,-5.6133727754925644E-7]
["A^2＝{x0^2＋2x0ζ(x'0/ω)＋(x'0/ω)^2}/(1－ζ^2)",null,null,null,0.31200000000000011,73.421264597590451,-0.2738399435242358,-0.72873584710541972,null,73.421443944801183,-0.27387737365292164,-0.72873689197495339,null,1.7934721073231685E-4,-3.7430128685844721E-5,-1.0448695336728875E-6]
["α＝atan2[x0,－(x'0+ζωx0)/{ω√(1－ζ^2)}]",null,null,null,0.32400000000000012,71.484423095491991,0.59659243614971824,-0.72677607967791424,null,71.484649583753949,0.59655604674155327,-0.72677761677237052,null,2.264882619584796E-4,-3.6389408164971826E-5,-1.5370944562720368E-6]
[null,null,null,null,0.33600000000000013,68.577610948959006,1.4379046514294391,-0.7145342025181789,null,68.577883231615658,1.4378699617740744,-0.71453623155163815,null,2.7228265665257823E-4,-3.4689655364683603E-5,-2.0290334592498738E-6]
["減衰振動理論値",null,null,null,0.34800000000000014,64.765140508075874,2.2388309508875937,-0.69242802409851067,null,64.765456330508528,2.238798614412274,-0.69243053559333079,null,3.1582243265404486E-4,-3.233647531963868E-5,-2.5114948201121479E-6]
["x''+2ζωx'+ω^2x=0",null,"運動方程式",null,0.36000000000000015,60.122669771479785,2.988946687170408,-0.66100563145820601,null,60.123025993152396,2.9889173388806811,-0.66100860670913764,null,3.5622167261095683E-4,-2.9348289726893739E-5,-2.9752509316249842E-6]
["x＝Ae^(－ζωt)cos{ω√(1－ζ^2)t＋α}",null,"解析解",null,0.37200000000000016,54.735858118089006,3.678796520773024,-0.62093451159635049,null,54.736250751964576,3.6787707646550198,-0.62093792281274618,null,3.9263387557042506E-4,-2.5756118004149897E-5,-3.4112163956878661E-6]
["x'＝－ζωx－Aω√(1－ζ^2)e^(－ζωt)sin{ω√(1－ζ^2)t＋α}",null,null,null,0.38400000000000017,48.698911782500872,4.3000058082268895,-0.57298923398954649,null,48.69933605110424,4.2999842051075756,-0.57299304461319389,null,4.2426860336775007E-4,-2.1603119313873265E-5,-3.8106236474044763E-6]
["x''＝－2ζωx'－ω^2x",null,null,null,0.39600000000000019,42.113042359698937,4.8453739904747168,-0.5180379034064837,null,42.113492766796504,4.845357046569486,-0.51804206859935475,null,4.5040709756705155E-4,-1.6943905230881739E-5,-4.1651928710528807E-6]
[null,null,null,null,0.4080000000000002,35.084862308489996,5.3089490810961779,-0.45702760470682352,null,35.085332725074657,5.3089372374593156,-0.45703207199993284,null,4.7041658466184799E-4,-1.1843636862352014E-5,-4.4672931093225898E-6]
["計算用",null,null,null,0.42000000000000021,27.72474175001792,5.6860826439978931,-0.39096907038013706,null,27.725225513030736,5.6860762670739815,-0.39097378047178699,null,4.8376301281649603E-4,-6.3769239115885057E-6,-4.7100916499287493E-6]
["x＝Ae^(－γt)cos(ωdt＋α)",null,null,null,0.43200000000000022,20.145150831585077,5.9734649419303656,-0.32092080715445809,null,20.145640853580005,5.9734643153837084,-0.32092569484347422,null,4.9002199492775844E-4,-6.2654665722305936E-7,-4.8876890161309028E-6]
["x'＝－γx－Aωde^(－γt)sin(ωdt＋α)",null,null,null,0.44400000000000023,12.459011555600371,6.1691402265531545,-0.24797292008706681,null,12.459500443365858,6.1691455445284635,-0.24797791532422786,null,4.8888776548672297E-4,5.3179753090049076E-6,-4.9952371610484381E-6]
["x''＝－2γx'－ω^2x",null,null,null,0.45600000000000024,4.7780822721913694,6.2725024236824964,-0.17323087119556363,null,4.7785624521884298,6.2725137856236026,-0.17323590023435637,null,4.8017999706040371E-4,1.1361941106180495E-5,-5.0290387927365288E-6]
[null,null,null,null,0.46800000000000025,-2.7886029803185401,6.2842717399548738,-9.7799404995912068E-2,null,-2.7881391319578874,6.2842891470797353,-9.7804391622015832E-2,null,4.6384836065271884E-4,1.740712486153484E-5,-4.9866261037645465E-6]
["1－ζ^2＜0","過減衰","ζ>1",null,0.48000000000000026,-10.136219408420539,6.2064529757961644,-2.2766865431717895E-2,null,-10.135779433665087,6.2064763292964953,-2.2771732249279034E-2,null,4.399747554515443E-4,2.3353500330891563E-5,-4.8668175611395192E-6]
["1－ζ^2=0","臨界減衰","ζ=1",null,0.49200000000000027,-17.165541362581042,6.0422765709539572,5.0809882206731279E-2,null,-17.165132589405975,6.0423056719567789,5.0805212454924177E-2,null,4.087731750672674E-4,2.910100282171868E-5,-4.6697518071014965E-6]
["1－ζ^2＞0","減衰振動","0<ζ<1",null,0.50400000000000023,-23.784219703649754,5.7961236299099443,0.12191972443829867,null,-23.783849116430446,5.7961581812069678,0.1219153275401651,null,3.705872193080495E-4,3.4551297023455163E-5,-4.3968981335712476E-6]
[null,"単振動","ζ=0",null,0.51600000000000024,-29.907931151846121,5.4734363725801112,0.18961058406685899,null,-29.907605266544522,5.4734759820996155,0.1896065330234529,null,3.2588530159927132E-4,3.9609519504324453E-5,-4.0510434060891942E-6]
[null,null,null,null,0.52800000000000025,-35.461386320183983,5.080615628562315,0.25300155063059354,null,-35.461111066541712,5.0806598145274977,0.25299791437486713,null,2.7525364227187765E-4,4.4185965182741427E-5,-3.6362557264135731E-6]
[null,null,null,null,0.54000000000000026,-40.379185457857446,4.6249071389456624,0.31129371179966125,null,-40.378966070681521,4.6249553366340459,0.3112905539741343,null,2.1938717592462353E-4,4.8197688383488924E-5,-3.1578255269559818E-6]
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{"sheet":"減衰振動＋外力","index":3,"n_rows":508,"n_cols":16,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,5,1,6]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,null,null,"単振動",null,null,null,"マクロで計算➡",null,{"$f":"exe(\"ルンゲ･クッタ･ギル法\",\"ForcedOscillation\",C8:C18,J8:L8)","v":"ルンゲ･クッタ･ギル法"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,null,null,null,null,null,null,"マクロは標準モジュール-Module6 の中。　実行させるには =exe(･･･ 　と先頭に＝を付加する。"]
["ダンパ＋バネ＋動摩擦＋外力",null,null,null,null,null,"解析解",null,null,null,"数値積分",null,null,null,"理論値との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"加速度","速度","変位",null,"加速度","速度","変位"]
[null,null,null,null,"t","理論値x''","理論値x'","理論値x",null,"x''","x'","x",null,"x''","x'","x"]
[null,null,null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]",null,"[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",0,{"$f":"-2*$C$30*G8-$C$25^2*H8","v":-100},{"$f":"-$C$30*H8-$C$31*$C$27*EXP(-$C$30*E8)*SIN($C$27*E8+$C$32)","v":0},{"$f":"$C$31*EXP(-$C$30*E8)*COS($C$27*E8+$C$32)","v":1},null,-100,0,1,null,{"$f":"J8-F8","v":0},{"$f":"K8-G8","v":0},0]
["終了時間","TL",6,"[s]",{"$f":"E8+$C$8","v":1.2E-2},-96.920839204435737,-1.1828708727782158,0.99286580949992165,null,-96.920851302399996,-1.182869068800001,0.99286589439999995,null,{"$f":"J9-F9","v":-1.2097964258828142E-5},1.8039782148093764E-6,8.4900078300975679E-8]
["重力加速度","g",9.8000000000000007,"[m/s^2]",2.4E-2,-92.537307219253776,-2.3208804232363018,0.97179068065726382,null,-92.537334937895537,-2.3208771272259408,0.97179089192347412,null,-2.7718641760543505E-5,3.296010361086843E-6,2.1126621030376214E-7]
["質量","m",10,"[kg]",3.6000000000000004E-2,-86.942632882240261,-3.3989196737188783,0.93740472229678018,null,-86.942679028080605,-3.3989152567879088,0.93740509541656425,null,-4.6145840343569944E-5,4.4169309694197523E-6,3.7311978406950885E-7]
["粘性係数","c",20,"[Ns/m]",4.8000000000000001E-2,-80.24504633494405,-4.4030902136626189,0.89051226762269298,null,-80.245112934402073,-4.4030850942297635,0.89051283122861602,null,-6.6599458023119951E-5,5.1194328554160506E-6,5.6360592304294244E-7]
["バネ定数","k",1000,"[N/m]",0.06,-72.565885163859775,-5.3208730092327556,0.83207631182325281,null,-72.565973419336061,-5.320867640326413,0.8320770869998888,null,{"$f":"J13-F13","v":-8.825547628532604E-5},{"$f":"K13-G13","v":5.3689063426176631E-6},{"$f":"L13-H13","v":7.7517663599202535E-7}]
["動摩擦係数","μ'",0,"[ND]",7.1999999999999995E-2,-64.037559176566816,-6.1412736067351483,0.76320106390037112,null,-64.037669442972842,-6.1412684627476581,0.76320206368468158,null,{"$f":"J14-F14","v":-1.1026640602551652E-4},5.1439874901859639E-6,9.9978431045144589E-7]
["強制力","f",0,"[N]",8.3999999999999991E-2,-54.80140608879708,-6.8549422260493182,0.68511290540895708,null,-54.801537870565014,-6.8549377892377823,0.68511413449040581,null,-1.3178176793360308E-4,4.4368115359461058E-6,1.229081448728131E-6]
["強制力角速度","Ω",0,"[rad/s]",9.5999999999999988E-2,-45.00547118332166,-7.4542676328389419,0.59914006448999546,null,-45.005623151521107,-7.4542643798655615,0.59914151911252234,null,-1.519681994466282E-4,3.2529733804409489E-6,1.4546225268752266E-6]
["初期位置","x0",1,"[m]",0.10799999999999998,-34.802244298007238,-7.9334440772918065,0.50669132452590848,null,-34.802414326803692,-7.9334424660893168,0.50669299258982325,null,-1.7002879645389157E-4,1.6112024896486332E-6,1.6680639147725884E-6]
["初期速度","x'0",0,"[m/s]",0.11999999999999998,-24.346387315763192,-8.2885109867969309,0.40923409289357054,null,-24.346572537085098,-8.2885114440320944,0.40923595425149289,null,-1.8522132190668117E-4,-4.5723516350903992E-7,1.8613579223503152E-6]
[null,null,null,null,0.13199999999999998,-13.792484677415661,-8.5173654945870645,0.30827215666589791,null,-13.792681552358811,-8.5173684039776951,0.30827418360314202,null,-1.9687494314979403E-4,-2.9093906306343342E-6,2.0269372441039657E-6]
[null,"c/m",{"$f":"C12/C11","v":2},"[1/s]",0.14399999999999999,-3.2928483401412016,-8.619748270471435,0.20532344881084072,null,-3.2930527453356007,-8.6197539621905506,0.20532560669716701,null,-2.044051943990155E-4,-5.691719115574756E-6,2.1578863262927683E-6]
[null,"k/m",{"$f":"C13/C11","v":100},"[1/s^2]",0.156,7.0045929148268744,-8.5972034881474606,0.10189814061468047,null,7.0043855879251407,-8.5972122295221105,0.1019003887111908,null,-2.073269017337509E-4,-8.7413746499009903E-6,2.2480965103238715E-6]
[null,"μ'g",{"$f":"C14*C10","v":0},"[s^2/m]",0.16800000000000001,16.958291829381583,-8.4530141113489048,-5.2263606683773829E-4,null,16.958086564530461,-8.4530260990320372,-5.2034366466386533E-4,null,-2.0526485112171144E-4,-1.1987683132375082E-5,2.2924021738729644E-6]
[null,"f/m",{"$f":"C15/C11","v":0},"[N/m]",0.18000000000000002,26.434942935271746,-8.192114003808209,-0.10050714927655328,null,26.434744973244968,-8.1921293575698257,-0.10050486258105315,null,-1.9796202677824226E-4,-1.5353761616765382E-5,2.2866955001338285E-6]
["振動中心","p＝mg/k",{"$f":"C11*C10/C13","v":9.8000000000000004E-2},"[m]",0.19200000000000003,35.311181577662339,-7.8209786616898089,-0.19669224254282716,null,35.310996292365189,-7.8209974199393848,-0.19669001452486415,null,-1.8528529714956221E-4,-1.875824957586758E-5,2.2280179630129737E-6]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":10},"［rad/s］",0.20400000000000004,43.475101373605277,-7.3474966283042713,-0.28780108116996733,null,43.474934145130149,-7.3475187454207074,-0.28779896654288734,null,-1.6722847512795624E-4,-2.2117116436071171E-5,2.114627079996545E-6]
["〝","〝",{"$f":"DEGREES(C25)","v":572.95779513082323},"[deg/s]",0.21600000000000005,50.827572845734679,-6.7808238766000875,-0.37265925092534502,null,50.827428933004256,-6.7808492221089818,-0.37265730488786292,null,-1.4391273042235753E-4,-2.5345508894325519E-5,1.9460374821034243E-6]
["減衰固有角振動数","ωd＝ω√(1-ζ^2)",{"$f":"C25*SQRT(1-C29^2)","v":9.9498743710661994},"［rad/s］",0.22800000000000006,57.283349206401283,-6.1312236327846152,-0.45020901940832053,null,57.283233622019353,-6.1312519923859679,-0.45020729637247414,null,-1.1558438193048914E-4,-2.8359601352612174E-5,1.7230358463904416E-6]
["〝","〝",{"$f":"DEGREES(C27)","v":570.08580814747756},"[deg/s]",0.24000000000000007,62.771948624961965,-5.4098942626753956,-0.51952160099611178,null,62.771866014815508,-5.4099253410887664,-0.5195201533263798,null,-8.2610146456829625E-5,-3.1078413370799751E-5,1.4476697319798504E-6]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0.1},"[ND]",0.25200000000000006,67.238305740419079,-4.62878794986021,-0.57980729840698664,null,67.238260270452301,-4.6288213754194905,-0.5798061751961332,null,-4.5469966778455273E-5,-3.3425559280431116E-5,1.123210853437584E-6]
["減衰率","γ＝ζω",{"$f":"C29*C25","v":1},null,0.26400000000000007,70.643188632614908,-3.8004229608884588,-0.63042342710837995,null,70.643183885029771,-3.8004582917852905,-0.63042267301459187,null,-4.7475851374656486E-6,-3.5330896831720082E-5,7.540937880801124E-7]
["振幅","A＝x0",{"$f":"SQRT(($C$17^2+2*$C$17*$C$29*($C$18/$C$25)+($C$18/$C$25)^2)/(1-$C$29^2))","v":1.0050378152592121},"[m]",0.27600000000000008,72.963380888175436,-2.9376923175676324,-0.67087996253040172,null,72.963419769108,-2.9377290496117747,-0.67087961669884444,null,3.8880932564211435E-5,-3.6732044142340214E-5,3.4583155728018511E-7]
["初期位相","α＝0",{"$f":"ATAN2($C$17,-($C$18+$C$29*$C$25*$C$17)/($C$25*SQRT(1-$C$29^2)))","v":-0.1001674211615598},"[rad]",0.28800000000000009,74.191631744383599,-2.053671680623034,-0.70084288383137527,null,74.191716404864081,-2.0537092563601731,-0.70084297892143732,null,8.466048048205721E-5,-3.757573713913942E-5,-9.509006204666548E-8]
["〝","〝",{"$f":"DEGREES(C32)","v":-5.7391704772667866},"[deg]",0.3000000000000001,74.336380519379588,-1.1614291936856629,-0.72013522132008267,null,74.336512291113308,-1.1614670126886493,-0.72013578265736022,null,1.3177173372014295E-4,-3.781900298638341E-5,-5.6133727754925644E-7]
["A^2＝{x0^2＋2x0ζ(x'0/ω)＋(x'0/ω)^2}/(1－ζ^2)",null,null,null,0.31200000000000011,73.421264597590451,-0.2738399435242358,-0.72873584710541972,null,73.421443944801183,-0.27387737365292164,-0.72873689197495339,null,1.7934721073231685E-4,-3.7430128685844721E-5,-1.0448695336728875E-6]
["α＝atan2[x0,－(x'0+ζωx0)/{ω√(1－ζ^2)}]",null,null,null,0.32400000000000012,71.484423095491991,0.59659243614971824,-0.72677607967791424,null,71.484649583753949,0.59655604674155327,-0.72677761677237052,null,2.264882619584796E-4,-3.6389408164971826E-5,-1.5370944562720368E-6]
[null,null,null,null,0.33600000000000013,68.577610948959006,1.4379046514294391,-0.7145342025181789,null,68.577883231615658,1.4378699617740744,-0.71453623155163815,null,2.7228265665257823E-4,-3.4689655364683603E-5,-2.0290334592498738E-6]
["減衰振動理論値",null,null,null,0.34800000000000014,64.765140508075874,2.2388309508875937,-0.69242802409851067,null,64.765456330508528,2.238798614412274,-0.69243053559333079,null,3.1582243265404486E-4,-3.233647531963868E-5,-2.5114948201121479E-6]
["x''+2ζωx'+ω^2x=0",null,"運動方程式",null,0.36000000000000015,60.122669771479785,2.988946687170408,-0.66100563145820601,null,60.123025993152396,2.9889173388806811,-0.66100860670913764,null,3.5622167261095683E-4,-2.9348289726893739E-5,-2.9752509316249842E-6]
["x＝Ae^(－ζωt)cos{ω√(1－ζ^2)t＋α}",null,"解析解",null,0.37200000000000016,54.735858118089006,3.678796520773024,-0.62093451159635049,null,54.736250751964576,3.6787707646550198,-0.62093792281274618,null,3.9263387557042506E-4,-2.5756118004149897E-5,-3.4112163956878661E-6]
["x'＝－ζωx－Aω√(1－ζ^2)e^(－ζωt)sin{ω√(1－ζ^2)t＋α}",null,null,null,0.38400000000000017,48.698911782500872,4.3000058082268895,-0.57298923398954649,null,48.69933605110424,4.2999842051075756,-0.57299304461319389,null,4.2426860336775007E-4,-2.1603119313873265E-5,-3.8106236474044763E-6]
["x''＝－2ζωx'－ω^2x",null,null,null,0.39600000000000019,42.113042359698937,4.8453739904747168,-0.5180379034064837,null,42.113492766796504,4.845357046569486,-0.51804206859935475,null,4.5040709756705155E-4,-1.6943905230881739E-5,-4.1651928710528807E-6]
[null,null,null,null,0.4080000000000002,35.084862308489996,5.3089490810961779,-0.45702760470682352,null,35.085332725074657,5.3089372374593156,-0.45703207199993284,null,4.7041658466184799E-4,-1.1843636862352014E-5,-4.4672931093225898E-6]
["計算用",null,null,null,0.42000000000000021,27.72474175001792,5.6860826439978931,-0.39096907038013706,null,27.725225513030736,5.6860762670739815,-0.39097378047178699,null,4.8376301281649603E-4,-6.3769239115885057E-6,-4.7100916499287493E-6]
["x＝Ae^(－γt)cos(ωdt＋α)",null,null,null,0.43200000000000022,20.145150831585077,5.9734649419303656,-0.32092080715445809,null,20.145640853580005,5.9734643153837084,-0.32092569484347422,null,4.9002199492775844E-4,-6.2654665722305936E-7,-4.8876890161309028E-6]
["x'＝－γx－Aωde^(－γt)sin(ωdt＋α)",null,null,null,0.44400000000000023,12.459011555600371,6.1691402265531545,-0.24797292008706681,null,12.459500443365858,6.1691455445284635,-0.24797791532422786,null,4.8888776548672297E-4,5.3179753090049076E-6,-4.9952371610484381E-6]
["x''＝－2γx'－ω^2x",null,null,null,0.45600000000000024,4.7780822721913694,6.2725024236824964,-0.17323087119556363,null,4.7785624521884298,6.2725137856236026,-0.17323590023435637,null,4.8017999706040371E-4,1.1361941106180495E-5,-5.0290387927365288E-6]
[null,null,null,null,0.46800000000000025,-2.7886029803185401,6.2842717399548738,-9.7799404995912068E-2,null,-2.7881391319578874,6.2842891470797353,-9.7804391622015832E-2,null,4.6384836065271884E-4,1.740712486153484E-5,-4.9866261037645465E-6]
["1－ζ^2＜0","過減衰","ζ>1",null,0.48000000000000026,-10.136219408420539,6.2064529757961644,-2.2766865431717895E-2,null,-10.135779433665087,6.2064763292964953,-2.2771732249279034E-2,null,4.399747554515443E-4,2.3353500330891563E-5,-4.8668175611395192E-6]
["1－ζ^2=0","臨界減衰","ζ=1",null,0.49200000000000027,-17.165541362581042,6.0422765709539572,5.0809882206731279E-2,null,-17.165132589405975,6.0423056719567789,5.0805212454924177E-2,null,4.087731750672674E-4,2.910100282171868E-5,-4.6697518071014965E-6]
["1－ζ^2＞0","減衰振動","0<ζ<1",null,0.50400000000000023,-23.784219703649754,5.7961236299099443,0.12191972443829867,null,-23.783849116430446,5.7961581812069678,0.1219153275401651,null,3.705872193080495E-4,3.4551297023455163E-5,-4.3968981335712476E-6]
[null,"単振動","ζ=0",null,0.51600000000000024,-29.907931151846121,5.4734363725801112,0.18961058406685899,null,-29.907605266544522,5.4734759820996155,0.1896065330234529,null,3.2588530159927132E-4,3.9609519504324453E-5,-4.0510434060891942E-6]
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[null,null,null,null,0.54000000000000026,-40.379185457857446,4.6249071389456624,0.31129371179966125,null,-40.378966070681521,4.6249553366340459,0.3112905539741343,null,2.1938717592462353E-4,4.8197688383488924E-5,-3.1578255269559818E-6]
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[null,null,null,null,0.64800000000000035,-50.744304918082008,-0.86005977312336035,0.52464424464328729,null,-50.744672144217041,-0.8600095815058667,0.52464691307228772,null,-3.672261350331496E-4,5.0191617493644536E-5,2.6684290004297395E-6]
[null,null,null,null,0.66000000000000036,-48.164466520586977,-1.4541635453302,0.5107279361124738,null,-48.164889499952061,-1.4541172131923055,0.51073123926336672,null,-4.2297936508362E-4,4.6332137894511405E-5,3.3031508929193265E-6]
[null,null,null,null,0.67200000000000037,-44.961317448065358,-2.0135127110805877,0.48988342870226531,null,-44.961790658318975,-2.0134709673552464,0.48988732593029466,null,-4.7321025361668489E-4,4.1743725341270022E-5,3.8972280293481099E-6]
[null,null,null,null,0.68400000000000039,-41.195160650129402,-2.5309822559359247,0.4625712516200125,null,-41.195677738634366,-2.5309457673274638,0.4625756927328929,null,-5.1708850496368086E-4,3.6488608460949479E-5,4.4411128803933941E-6]
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[null,null,null,null,0.73200000000000043,-21.912932549385765,-4.0677308351347419,0.3004839421965525,null,-21.913548543036004,-4.0677204269256002,0.30048989396887205,null,-6.1599365023923269E-4,1.0408209141665736E-5,5.9517723195456895E-6]
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[null,null,null,null,0.76800000000000046,{"$f":"-2*$C$30*G72-$C$25^2*H72","v":-5.2257901372129982},{"$f":"-$C$30*H72-$C$31*$C$27*EXP(-$C$30*E72)*SIN($C$27*E72+$C$32)","v":-4.557913069397352},{"$f":"$C$31*EXP(-$C$30*E72)*COS($C$27*E72+$C$32)","v":0.14341616276007702},null,-5.2263891540091816,-4.5579247996629748,0.14342238753335132,null,-5.9901679618334924E-4,-1.1730265622844627E-5,6.2247732743048179E-6]
[null,null,null,null,{"$f":"E72+$C$8","v":0.78000000000000047},0.32654295439581382,-4.5872103986830846,8.8478778429703545E-2,null,0.32596740299577043,-4.5872294235432127,8.8484914440906545E-2,null,-5.7555140004339478E-4,-1.9024860128169507E-5,6.1360112030006686E-6]
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{"sheet":"動摩擦","index":4,"n_rows":508,"n_cols":10,"rows_kept":508,"cut":false,"hidden":false,"merged":[]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,null,null,null,null,"マクロで計算 ➡",null,{"$f":"exe(\"ルンゲ･クッタ･ギル法\",\"ForcedOscillation\",C8:C18,G8:I8)","v":"ルンゲ･クッタ･ギル法"}]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",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,null,null,"動摩擦力"]
[null,null,null,null,null,"時間","加速度","速度","変位"]
[null,null,null,null,null,"t","x''","x'","x"]
[null,null,null,null,null,"[s]","[m/s^2]","[m/s]","[m]"]
["時間間隔","Δt",{"$f":"C9/500","v":1.2E-2},"[s]",null,0,-100,0,1]
["終了時間","TL",6,"[s]",null,{"$f":"F8+$C$8","v":1.2E-2},-94.404383999999993,-1.1481905600000009,0.99304384000000001]
["重力加速度","g",9.8000000000000007,"[m/s^2]",null,2.4E-2,-92.350966205890558,-2.27006727007524,0.97250966205890566]
["質量","m",10,"[kg]",null,3.6000000000000004E-2,-88.969294231203705,-3.3592942857558699,0.93869294231203704]
["粘性係数","c",0,"[Ns/m]",null,4.8000000000000001E-2,-84.308005632077112,-4.4002056063016424,0.89208005632077114]
["バネ定数","k",1000,"[N/m]",null,0.06,-78.434142277278994,-5.3778301407354316,0.83334142277279]
["動摩擦係数","μ'",0.5,"[ND]",null,7.1999999999999995E-2,-71.432186105794642,-6.2781070322043151,0.76332186105794653]
["強制力","f",0,"[N]",null,8.3999999999999991E-2,-63.402844049528461,-7.088087890726892,0.68302844049528455]
["強制力角速度","Ω",0,"[rad/s]",null,9.5999999999999988E-2,-54.461599597197456,-7.7961230256787495,0.59361599597197456]
["初期位置","x0",1,"[m]",null,0.10799999999999998,-44.73705183181761,-8.3920289994947748,0.49637051831817608]
["初期速度","x'0",0,"[m/s]",null,0.11999999999999998,-34.369065830881162,-8.8672350927180226,0.39269065830881161]
[null,null,null,null,null,0.13199999999999998,-23.506761031432994,-9.2149065738362985,0.28406761031432992]
[null,"c/m",{"$f":"C12/C11","v":0},"[1/s]",null,0.14399999999999999,-12.306366492751069,-9.4300430009569673,0.17206366492751068]
[null,"k/m",{"$f":"C13/C11","v":100},"[1/s^2]",null,0.156,-0.92897390370414623,-9.5095501414796271,5.8289739037041467E-2]
[null,"μ'g",{"$f":"C14*C10","v":4.9000000000000004},"[s^2/m]",null,0.16800000000000001,10.461779347436096,-9.4522844753702184,-5.5617793474360952E-2]
[null,"f/m",{"$f":"C15/C11","v":0},"[N/m]",null,0.18000000000000002,21.702063717063318,-9.2590696419613927,-0.1680206371706332]
["振動中心","p＝mg/k",{"$f":"C11*C10/C13","v":9.8000000000000004E-2},"[m]",null,0.19200000000000003,32.630213813915802,-8.9326845937312687,-0.27730213813915805]
["固有角振動数","ω＝√(k/m)",{"$f":"SQRT(C13/C11)","v":10},"［rad/s］",null,0.20400000000000004,43.089053580350551,-8.4778236274421452,-0.38189053580350552]
["〝","〝",{"$f":"DEGREES(C25)","v":572.95779513082323},"[deg/s]",null,0.21600000000000005,52.928156904878506,-7.9010288674996092,-0.48028156904878511]
["減衰比","ζ＝c/{2√(mk)} ",{"$f":"C12/(2*SQRT(C11*C13))","v":0},"[ND]",null,0.22800000000000006,62.006011152300196,-7.2105961726033456,-0.57106011152300196]
["振幅","A＝x0",{"$f":"SQRT(C17^2+C18^2/(C25*SQRT(1-C27^2)*(1+2*C27^2/(1-2*C27^2)))^2)","v":1},"[m]",null,0.24000000000000007,70.192052494086923,-6.4164558190051171,-0.65292052494086916]
["初期位相","α＝0",{"$f":"ATAN2(C17,-C18/(C25*SQRT(1-C27^2)*(1+2*C27^2/(1-2*C27^2))))","v":0},"[rad]",null,0.25200000000000006,77.368543765510452,-5.5300296764693435,-0.7246854376551044]
["〝","〝",{"$f":"DEGREES(C29)","v":0},"[deg]",null,0.26400000000000007,83.432267840911891,-4.5640669311294904,-0.78532267840911885]
[null,null,null,null,null,0.27600000000000008,88.296012171845206,-3.5324607179865177,-0.83396012171845202]
["減衰振動理論値",null,null,null,null,0.28800000000000009,91.889823136469104,-2.4500483003660247,-0.86989823136469102]
["x''+2ζωx'+ω^2=0",null,"運動方程式",null,null,0.3000000000000001,94.162012159292615,-1.3323976702894049,-0.89262012159292614]
["x＝Ae^(－ζωt)cos{ω√(1－ζ^2)t＋α}",null,"理論値",null,null,0.31200000000000011,95.07989913058762,-0.19558363901786799,-0.90179899130587615]
["x'＝－Aζωe^(－ζωt)cos{ω√(1－ζ^2)t＋α}",null,null,null,null,0.32400000000000012,84.877322433116944,0.84618448181251049,-0.89777322433116946]
["－Aω√(1－ζ^2)e^(－ζωt)sin{ω√(1－ζ^2)t＋α}",null,null,null,null,0.33600000000000013,83.253954684796923,1.8561826668887136,-0.88153954684796931]
["x''＝－Aω^2(1－2ζ^2)e^(－ζωt)cos{ω√(1－ζ^2)t＋α}",null,null,null,null,0.34800000000000014,80.433172131049048,2.8394839314279983,-0.85333172131049051]
["＋2Aζω^2√(1－ζ^2)e^(－ζωt)sin{ω√(1－ζ^2)t＋α}",null,null,null,null,0.36000000000000015,76.455545230321604,3.781945770478099,-0.81355545230321613]
[null,null,null,null,null,0.37200000000000016,71.378282959819344,4.67001306000334,-0.76278282959819343]
["A^2＝{x0^2＋x'0^2/[ω√(1－ζ^2){1＋2ζ^2/(1－2ζ^2)}]^2",null,null,null,null,0.38400000000000017,65.274409996482191,5.4909130158527439,-0.70174409996482201]
["α＝atan2(x0,－x'0/[Aω√(1－ζ^2){1＋2ζ^2/(1－2ζ^2)}])",null,null,null,null,0.39600000000000019,58.231716425872257,6.2328389005769491,-0.63131716425872253]
[null,null,null,null,null,0.4080000000000002,50.351495084977223,6.8851198358982986,-0.5525149508497722]
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["(ζω)^2-ω^2=0","臨界減衰","ζ=1",null,null,0.43200000000000022,32.542239768059169,7.8846449515778749,-0.37442239768059166]
["(ζω)^2-ω^2<0","減衰振動","0<ζ<1",null,null,0.44400000000000023,22.869350642247824,8.2175132919702847,-0.27769350642247825]
[null,"単振動","ζ=0",null,null,0.45600000000000024,12.867539396729716,8.4321917659914174,-0.17767539396729717]
[null,null,null,null,null,0.46800000000000025,2.6806588817099959,8.5255927270392675,-7.5806588817099965E-2]
[null,null,null,null,null,0.48000000000000026,-7.5447762667388316,8.4963728241304715,2.6447762667388311E-2]
[null,null,null,null,null,0.49200000000000027,-17.661696899708332,8.3449523228135494,0.12761696899708333]
[null,null,null,null,null,0.50400000000000023,-27.524594603778212,8.0735090605515722,0.22624594603778209]
[null,null,null,null,null,0.51600000000000024,-36.991614501695892,7.6859471235131345,0.32091614501695892]
[null,null,null,null,null,0.52800000000000025,-45.926595505333026,7.1878406952842848,0.41026595505333024]
[null,null,null,null,null,0.54000000000000026,-54.20102867661852,6.5863538851084025,0.49301028676618519]
[null,null,null,null,null,0.55200000000000027,-61.695905529975597,5.8901376887396539,0.56795905529975599]
[null,null,null,null,null,0.56400000000000028,-68.303429692727576,5.1092055638899145,0.63403429692727575]
[null,null,null,null,null,0.57600000000000029,-73.92856730521639,4.2547894098283976,0.69028567305216382]
[null,null,null,null,null,0.5880000000000003,-78.490413861734112,3.3391780225339267,0.73590413861734105]
[null,null,null,null,null,0.60000000000000031,-81.923357833441202,2.3755403488482054,0.77023357833441197]
[null,null,null,null,null,0.61200000000000032,-84.178024337265256,1.3777360817094204,0.79278024337265252]
[null,null,null,null,null,0.62400000000000033,-85.221985278303194,0.36011632061458804,0.80321985278303187]
[null,null,null,null,null,0.63600000000000034,-75.28726575198634,-0.56482395565245058,0.80187265751986347]
[null,null,null,null,null,0.64800000000000035,-74.069685866757482,-1.4620410190209092,0.78969685866757489]
[null,null,null,null,null,0.66000000000000036,-71.786785545912394,-2.3382299791664907,0.76686785545912406]
["x0＝Acos(α)",null,null,null,null,0.67200000000000037,-68.471399055149163,-3.1807888927507393,0.73371399055149167]
["x'0＝－Aω{ζcos(α)＋√(1－ζ^2)sin(α)}",null,null,null,null,0.68400000000000039,-64.171210575550163,-3.9775995071079695,0.69071210575550168]
["x''0＝－Aω^2{(1－2ζ^2)cos(α)－2ζ√(1－ζ^2)sin(α)}＝0",null,null,null,null,0.6960000000000004,-58.948068376716485,-4.7172015531585592,0.63848068376716482]
["(1－2ζ^2)cos(α)－2ζ√(1－ζ^2)sin(α)＝0",null,null,null,null,0.70800000000000041,-52.877095272397717,-5.3889575747485861,0.57777095272397716]
["cos(α)＝{2ζ√(1－ζ^2)/(1－2ζ^2)}sin(α)",null,null,null,null,0.72000000000000042,-46.045608152656563,-5.9832059237287707,0.50945608152656563]
["x'0＝－Aω√(1－ζ^2)sin(α){1＋2ζ^2/(1－2ζ^2)}",null,null,null,null,0.73200000000000043,-38.551862132597684,-6.4913997202941873,0.43451862132597679]
["sin(α)＝－x'0/[Aω√(1－ζ^2){1＋2ζ^2/(1－2ζ^2)}]",null,null,null,null,0.74400000000000044,-30.503637380173224,-6.9062297799634074,0.3540363738017322]
["cos(α)＝x0/A",null,null,null,null,0.75600000000000045,-22.016688948273142,-7.2217297391784987,0.26916688948273143]
["(x0/A)^2＋x'0^2/[Aω√(1－ζ^2){1＋2ζ^2/(1－2ζ^2)}]^2=1",null,null,null,null,0.76800000000000046,-13.213081906672722,-7.4333618675389275,0.18113081906672721]
["A^2＝{x0^2＋x'0^2/[ω√(1－ζ^2){1＋2ζ^2/(1－2ζ^2)}]^2",null,null,null,null,{"$f":"F72+$C$8","v":0.78000000000000047},-4.2194357191041423,-7.538082332460343,9.1194357191041422E-2]
["α＝atan2(x0,－x'0/[Aω√(1－ζ^2){1＋2ζ^2/(1－2ζ^2)}])",null,null,null,null,0.79200000000000048,4.8348968839837267,-7.5343849775785205,6.5103116016274032E-4]
[null,null,null,null,null,0.80400000000000049,13.819690344286926,-7.4223229852486146,-8.9196903442869249E-2]
[null,null,null,null,null,0.8160000000000005,22.605719268033461,-7.2035081115758892,-0.17705719268033462]
[null,null,null,null,null,0.82800000000000051,31.06661703324783,-6.8810875049811449,-0.2616661703324783]
[null,null,null,null,null,0.84000000000000052,39.080693280142647,-6.4596984417129075,-0.34180693280142649]
[null,null,null,null,null,0.85200000000000053,46.532684144258916,-5.9454016293318661,-0.41632684144258919]
[null,null,null,null,null,0.86400000000000055,53.315410059317031,-5.3455940374430018,-0.48415410059317032]
[null,null,null,null,null,0.87600000000000056,59.331317286136624,-4.6689025094037993,-0.54431317286136627]
[null,null,null,null,null,0.88800000000000057,64.493880996315269,-3.9250596851579744,-0.59593880996315263]
[null,null,null,null,null,0.90000000000000058,68.72884973056992,-3.1247640197574267,-0.63828849730569914]
[null,null,null,null,null,0.91200000000000059,71.9753133331035,-2.2795259108817052,-0.67075313333103492]
[null,null,null,null,null,0.9240000000000006,74.186579002247072,-1.4015021484539776,-0.69286579002247062]
[null,null,null,null,null,0.93600000000000061,75.330842857430682,-0.50332106741197091,-0.70430842857430676]
[null,null,null,null,null,0.94800000000000062,65.591647363559673,0.38249908159424745,-0.70491647363559684]
[null,null,null,null,null,0.96000000000000063,64.662056913817153,1.16495912191748,-0.69562056913817161]
[null,null,null,null,null,0.97200000000000064,62.802452920179554,1.930663897213176,-0.67702452920179557]
[null,null,null,null,null,0.98400000000000065,60.039581507715646,2.6686005224873668,-0.64939581507715649]
[null,null,null,null,null,0.99600000000000066,56.413180205364242,3.3681554935791378,-0.61313180205364237]
[null,null,null,null,null,1.0080000000000007,51.975406413289136,4.0192673377632895,-0.56875406413289131]
[null,null,null,null,null,1.0200000000000007,46.790087239241664,4.6125713246559599,-0.51690087239241667]
[null,null,null,null,null,1.0320000000000007,40.931801493300725,5.1395341560930916,-0.45831801493300722]
[null,null,null,null,null,1.0440000000000007,34.484807044371699,5.592576697780931,-0.39384807044371695]
[null,null,null,null,null,1.0560000000000007,27.541828965937562,5.9651829875091593,-0.32441828965937564]
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[null,null,null,null,null,1.0920000000000007,4.7625478746577361,6.5530227772026164,-9.6625478746577356E-2]
[null,null,null,null,null,1.1040000000000008,-3.1164559486709642,6.5629110444406553,-1.7835440513290359E-2]
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{"sheet":"振動","index":5,"n_rows":508,"n_cols":50,"rows_kept":508,"cut":false,"hidden":false,"merged":[[4,10,4,12],[4,14,4,16],[4,18,4,20]]}
["振動の運動方程式"]
["mx''+cx'+kx=-sign(x')μ'mg+fsinΩt",null,null,null,null,null,null,null,null,null,null,null,null,null,"ルンゲ･クッタ法による数値積分計算式をシートに記述して実行",null,null,null,null,null,null,null,null,null,null,null,null,"マクロで計算 ➡",null,"exe(\"ルンゲ･クッタ法\",\"ForcedOscillation_rk\",C8:C18,AA8:AC8)",null,null,null,null,null,null,null," ",null,"マクロで計算 ➡",null,"exe(\"ルンゲ･クッタ･ギル法\",\"ForcedOscillation\",C8:C18,AM8:AO8)",null,null,null,null,null,null,null," "]
["x''=-(c/m)x'-(k/m)x-sign(x')(μ'g)+(f/m)sinΩt",null,null,null,null,null,null,null,null,null,null,null,null,null,null,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。",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 理論値",null,null,null,null,null,null,null,null,"数値解析（その1）",null,null,null,null,null,null,null,null,"理論値との差",null,null,null,"数値解析（その2）",null,null,null,"理論値との差",null,null,null,"数値解析（その1）との差",null,null,null,"数値解析（その3）",null,null,null,"理論値との差",null,null,null,"数値解析（その1）との差"]
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[null,"技術的なご質問のみお受けします。"]
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[null,null,"sxsijk@Gmail.com","sxsijk@Gmail.com"]
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[null,null,{"$f":"SQRT(((C$139-C156)*COS(RADIANS(C157/2)))^2+(MAX(C$139,C156)*RADIANS(C157)-ABS(C$139-C156)*SIN(RADIANS(C157/2)))^2)","v":{"$error":"#REF!"}},null,{"$f":"C159-C$26","v":{"$error":"#REF!"}}]