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{"sheet":"水平運動","index":0,"n_rows":508,"n_cols":18,"rows_kept":508,"cut":false,"hidden":false,"merged":[[1,4,1,7]]}
["粘性抵抗と慣性抵抗を受ける物体の水平運動"]
["mv'＝－γv－kv^2",null,null,null,"粘性抵抗＋慣性抵抗",null,null,null,null,"マクロで計算➡",null,"exe(\"ルンゲ･クッタ･ギル法\",\"HorizontalMotion\",C8:C15,J8:M8)"]
["v'＝－(γ/m)v－(k/m)v^2",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,"解析解",null,null,null,null,"数値積分",null,null,null,null,"解析解との差"]
[null,null,null,null,"時間","加速度","速度","変位",null,"時間","加速度","速度","変位",null,"時間","加速度","速度","変位"]
[null,null,null,null,"t","解析解x''","解析解x'","解析解x",null,"t","x''","x'","x",null,"t","x''","x'","x"]
[null,null,null,null,"[s]","[m/s^2]","[m/s]","[m]",null,"[s]","[m/s^2]","[m/s]","[m]",null,"[s]","[m/s^2]","[m/s]","[m]"]
["積分間隔","Δt ",0.1,"[s]",0,{"$f":"-$C$16*G8-$C$17*G8^2","v":-10.1},{"$f":"$C$15*$C$16*EXP(-$C$16*E8)/($C$16+$C$15*$C$17*(1-EXP(-$C$16*E8)))","v":100},{"$f":"$C$14+(1/$C$17)*LN(1+$C$15*($C$17/$C$16)*(1-EXP(-$C$16*E8)))","v":0},null,0,-10.1,100,0,null,{"$f":"J8-E8","v":0},{"$f":"K8-F8","v":0},{"$f":"L8-G8","v":0},{"$f":"M8-H8","v":0}]
["出力時間間隔","To",10,"[s]",{"$f":"E8+$C$9","v":10},{"$f":"-$C$16*G9-$C$17*G9^2","v":-2.5123803653814241},49.62614452939129,690.6523836821367,null,10.000000000000007,-2.512380365955337,49.626144535115976,690.65238357040323,null,{"$f":"J9-E9","v":0},{"$f":"K9-F9","v":-5.7391291719000037E-10},{"$f":"L9-G9","v":5.72468650261726E-9},{"$f":"M9-H9","v":-1.1173347047588322E-7}]
["終了時間","TL",5000,"[s]",{"$f":"E9+$C$9","v":20},{"$f":"-$C$16*G10-$C$17*G10^2","v":-1.1147161349155228},32.89110862064215,1091.9678194338733,null,20.000000000000149,-1.1147161351020103,32.891108623434626,1091.96781935285,null,{"$f":"J10-E10","v":1.4921397450962104E-13},-1.8648749211536142E-10,2.7924755841013393E-9,-8.1023245002143085E-8]
["質量","m",10,"[kg]",30,-0.62647172999274858,24.534410917629927,1375.0935266130102,null,30.000000000000291,-0.6264717300730458,24.534410919233665,1375.0935265515695,null,2.9132252166164108E-13,-8.0297213322921834E-11,1.6037375871746917E-9,-6.1440687204594724E-8]
["粘性抵抗係数","γ",0.01,"[Ns/m]",40,-0.40071256915291736,19.524049769038164,1593.5231588454517,null,39.999999999999865,-0.40071256919431159,19.524049770071777,1593.5231587964518,null,-1.3500311979441904E-13,-4.1394221383939112E-11,1.0336123068555025E-9,-4.8999936552718282E-8]
["慣性抵抗係数","k",0.01,"[Ns^2/m^2]",50,-0.27815493062656899,16.185470644442997,1771.0562199815129,null,49.999999999999297,-0.27815493065059183,16.185470645162869,1771.0562199409828,null,-7.0343730840249918E-13,-2.4022839273385443E-11,7.198721618806303E-10,-4.0530039768782444E-8]
["初期変位","x0",0,"[m]",60,-0.20428824426145425,13.801686762807185,1920.3793721053846,null,59.999999999998728,-0.20428824427660261,13.801686763336784,1920.3793720709632,null,-1.2718714970105793E-12,-1.5148354792771102E-11,5.2959947538511187E-10,-3.4421418604324572E-8]
["初期速度","v0",100,"[m/s]",70,-0.15636089423822921,12.014427443484148,2049.0619714112649,null,69.999999999998167,-0.1563608942483839,12.014427443889868,2049.0619713814453,null,-1.8332002582610585E-12,-1.015468265030961E-11,4.0571990211901721E-10,-2.9819602787028998E-8]
[null,"a＝γ/m",{"$f":"C12/C11","v":1E-3},null,80,-0.12350986989995484,10.624741340811248,2161.9848158681757,null,79.999999999997598,-0.12350986990708965,10.624741341131921,2161.9848158419431,null,-2.4016344468691386E-12,-7.1348066343901451E-12,3.2067326571905141E-10,-2.6232555683236569E-8]
[null,"b＝k/m",{"$f":"C13/C11","v":1E-3},null,90,-0.10001612062888954,9.5132971906804773,2262.4796617723505,null,89.99999999999703,-0.10001612063409197,9.5132971909402535,2262.479661749001,null,-2.9700686354772188E-12,-5.2024357044544445E-12,2.5977620055073203E-10,-2.3349457478616387E-8]
[null,null,null,null,100,-8.2636030023930496E-2,8.6041765154202992,2352.922459286272,null,99.999999999996461,-8.2636030027839785E-2,8.6041765156349967,2352.922459265279,null,-3.5385028240852989E-12,-3.9092895587344856E-12,2.1469759303727187E-10,-2.099295670632273E-8]
[null,null,null,null,110,-6.9418694177311419E-2,7.8467774726124944,2435.067251520315,null,109.99999999999589,-6.9418694180322649E-2,7.8467774727928772,2435.0672515012861,null,-4.1069370126933791E-12,-3.0112301541151965E-12,1.8038281979215753E-10,-1.9028902897844091E-8]
["解析解",null,null,null,120,-5.9133575969214598E-2,7.2060739659838848,2510.2459092153022,null,119.99999999999532,-5.9133575971583197E-2,7.206073966137569,2510.2459091979399,null,-4.6753712013014592E-12,-2.3685983729926363E-12,1.5368417649597177E-10,-1.73622538568452E-8]
["v＝v0(γ/m)e^(-γt/m)/[(γ/m)＋v0(k/m){1－e^(-γt/m)}]",null,null,null,130,-5.0973377652056923E-2,6.6570509046713457,2579.4936066102159,null,129.99999999999531,-5.0973377653953357E-2,6.6570509048038327,2579.4936065942779,null,-4.6895820560166612E-12,-1.8964343984073651E-12,1.3248691033140858E-10,-1.5937985153868794E-8]
["x＝x0＋(m/k)ln[1＋v0(k/γ){1－e^(-γt/m)}]",null,null,null,140,-4.4390652909858712E-2,6.1813660960808541,2643.6308878009272,null,139.99999999999758,-4.4390652911400527E-2,6.1813660961962356,2643.6308877862239,null,-2.4158453015843406E-12,-1.5418152865542822E-12,1.1538148214640387E-10,-1.4703346096212044E-8]
[null,null,null,null,150,-3.9003536969907611E-2,5.7652643176411651,2703.31918463792,null,149.99999999999986,-3.9003536971178081E-2,5.7652643177425551,2703.3191846242962,null,0,-1.2704698404419901E-12,1.013900075008678E-10,-1.3623775885207579E-8]
["計算式",null,null,null,160,-3.4539091342178481E-2,5.3982278136893358,2759.0994689316967,null,160.00000000000213,-3.453909134323771E-2,5.398227813779128,2759.0994689190311,null,2.1316282072803006E-12,-1.0592290933253423E-12,8.9792173696423561E-11,-1.2665623216889799E-8]
["v'＝－av－bv^2",null,null,null,170,-3.0798039317800643E-2,5.0720767508892628,2811.4198366945388,null,170.00000000000441,-3.0798039318693047E-2,5.072076750969341,2811.4198366827181,null,4.4053649617126212E-12,-8.9240420608760473E-13,8.0078166320163291E-11,-1.1820702638942748E-8]
["v＝v0ae^(-at)/[a＋v0b{1－e^(-at)}]",null,null,null,180,-2.7632136407777477E-2,{"$f":"$C$15*$C$16*EXP(-$C$16*E26)/($C$16+$C$15*$C$17*(1-EXP(-$C$16*E26)))","v":4.780353814639458},{"$f":"$C$14+(1/$C$17)*LN(1+$C$15*($C$17/$C$16)*(1-EXP(-$C$16*E26)))","v":2860.6556224250071},null,180.00000000000668,-2.7632136408536311E-2,4.7803538147113125,2860.6556224139431,null,6.6791017161449417E-12,-7.5883396788434254E-13,7.1854522332159831E-11,-1.1064003047067672E-8]
["x＝x0＋(1/b)ln[1＋v0(b/a){1－e^(-at)}]",null,null,null,190,-2.492925490055389E-2,{"$f":"$C$15*$C$16*EXP(-$C$16*E27)/($C$16+$C$15*$C$17*(1-EXP(-$C$16*E27)))","v":4.5178934724198649},{"$f":"$C$14+(1/$C$17)*LN(1+$C$15*($C$17/$C$16)*(1-EXP(-$C$16*E27)))","v":2907.1243467019158},null,190.00000000000895,-2.4929254901204439E-2,4.5178934724846878,2907.1243466915334,null,8.9528384705772623E-12,-6.5054905906691829E-13,6.482281378339394E-11,-1.0382336768088862E-8]
[null,null,null,null,200,-2.2603317296324671E-2,4.2805143338687595,2951.0970121497348,null,200.00000000001123,-2.2603317296886586E-2,4.2805143339275311,2951.0970121399728,null,1.1226575225009583E-11,-5.6191509778535931E-13,5.8771654209976987E-11,-9.7620613814797252E-9]
[null,null,null,null,210,-2.0587357332389845E-2,4.0647954316036818,2992.8067685833666,null,210.0000000000135,-2.0587357332878482E-2,4.0647954316572044,2992.8067685741657,null,1.3500311979441904E-11,-4.8863690871314702E-13,5.3522519749549247E-11,-9.2009031504858285E-9]
[null,null,null,null,220,-1.8828645422194659E-2,3.8679108761734891,3032.4556499826931,null,220.00000000001577,-1.8828645422622279E-2,3.8679108762224392,3032.4556499740083,null,1.5774048733874224E-11,-4.2761974516913881E-13,4.8950177244933002E-11,-8.6847649072296917E-9]
["最終値(t→∞)","時間","∞","[s]",230,-1.7285205292602135E-2,3.6875058558289964,3070.219876301991,null,230.00000000001805,-1.7285205292978507E-2,3.687505855873936,3070.2198762937737,null,1.8047785488306545E-11,-3.7637254424183197E-13,4.4939607590777086E-11,-8.2172846305184066E-9]
["v＝0","速度",0,"[m/s]",240,-1.5923285881884058E-2,3.5216024022625678,3106.2540720473753,null,240.00000000002032,-1.5923285882217027E-2,3.5216024023039654,3106.2540720395891,null,2.0321522242738865E-11,-3.3296976287289226E-13,4.1397552053012987E-11,-7.7861841418780386E-9]
["x＝(1/b)ln{1＋v0(b/a)}","位置",{"$f":"(1/C17)*LN(1+C15*(C13/C12))","v":4615.1205168412598},"[m]",250,-1.4715500429182467E-2,3.3685269068706845,3140.6946568113958,null,250.0000000000226,-1.4715500429478482E-2,3.3685269069089441,3140.694656804008,null,2.2595258997171186E-11,-2.9601494866415834E-13,3.8259617696212445E-11,-7.3878254625014961E-9]
[null,null,null,null,260,-1.3639438855087031E-2,3.2268537474774925,3173.6625954583346,null,260.00000000002484,-1.3639438855351356E-2,3.2268537475129548,3173.6625954513152,null,2.4840574042173102E-11,-2.6432502020501403E-13,3.54622997633669E-11,-7.0194801082834601E-9]
["解析解の最終値","時間",{"$f":"E508","v":5000},"[s]",270,-1.2676620700111364E-2,3.0953609971894847,3205.265647819876,null,270.00000000002711,-1.2676620700348324E-2,3.0953609972224378,3205.2656478132039,null,2.7114310796605423E-11,-2.369597573714799E-13,3.2953195727714046E-11,-6.6720531322062016E-9]
[null,"速度",{"$f":"G508","v":6.7160389241586564E-3},"[m/s]",280,-1.1811696343439631E-2,2.9729952985052588,3235.6002233708723,null,280.00000000002939,-1.1811696343652905E-2,2.9729952985359631,3235.6002233645218,null,2.9388047551037744E-11,-2.1327384303049257E-13,3.0704327969033329E-11,-6.3505467551294714E-9]
[null,"位置",{"$f":"H508","v":4608.4269300363721},"[m]",290,-1.1031831429394508E-2,2.8588437637667083,3264.7529213021244,null,290.00000000003166,-1.1031831429587143E-2,2.8588437637953841,3264.7529212960721,null,3.1661784305470064E-11,-1.9263410311332052E-13,2.8675728458438243E-11,-6.052232492947951E-9]
[null,null,null,null,300,-1.0326228005828575E-2,2.7521113151041701,3292.8018179326373,null,300.00000000003394,-1.0326228006003173E-2,2.7521113151310139,3292.8018179268652,null,3.3935521059902385E-11,-1.7459818313358966E-13,2.6843860467806735E-11,-5.7721081248018891E-9]
[null,null,null,null,310,-9.6857487445046082E-3,2.6521022738015034,3319.8175496262133,null,310.00000000003621,-9.6857487446633615E-3,2.6521022738266855,3319.817549620695,null,3.6209257814334705E-11,-1.587532189040175E-13,2.5182078644547801E-11,-5.5183591030072421E-9]
[null,null,null,null,320,-9.1026196419831083E-3,2.5582052975533065,3345.8642289942791,null,320.00000000003848,-9.1026196421278432E-3,2.5582052975769698,3345.8642289890045,null,3.8482994568767026E-11,-1.4473491849464892E-13,2.3663293546860587E-11,-5.2746145229320973E-9]
[null,null,null,null,330,-8.570193013042E-3,2.4698809762416407,3371.0002242656938,null,330.00000000004076,-8.5701930131743403E-3,2.4698809762639211,3371.0002242606479,null,4.0756731323199347E-11,-1.3234031925879464E-13,2.2280399747387492E-11,-5.0458766054362059E-9]
[null,null,null,null,340,-8.0827571968254477E-3,2.3866515544529179,3395.2788256368285,null,340.00000000004303,-8.0827571969467587E-3,2.3866515544739304,3395.2788256319973,null,4.3030468077631667E-11,-1.213109473985341E-13,2.1012525053265563E-11,-4.8312358558177948E-9]
[null,null,null,null,350,-7.6353827424183191E-3,2.3080923671450551,3418.7488177162336,null,350.0000000000453,-7.6353827425298341E-3,2.3080923671649112,3418.7488177116056,null,4.5304204832063988E-11,-1.1151496392969307E-13,1.9856116750816E-11,-4.6279637899715453E-9]
[null,null,null,null,360,-7.2237972951999414E-3,2.233824664311876,3441.4549735098835,null,360.00000000004758,-7.2237972953026535E-3,2.2338246643306614,3441.4549735054525,null,4.7577941586496308E-11,-1.0271210965084876E-13,1.8785417665867499E-11,-4.4310581870377064E-9]
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[null,null,null,null,380,-6.4935933769756041E-3,2.096842963480003,3484.737323148056,null,380.00000000005213,-6.4935933770632944E-3,2.0968429634968868,3484.7373231439765,null,5.212541509536095E-11,-8.7690271710627599E-14,1.6883827669289531E-11,-4.0795384848024696E-9]
[null,null,null,null,390,-6.1688814106319627E-3,2.0335511462435414,3505.3865881106103,null,390.0000000000544,-6.1688814107132457E-3,2.0335511462595828,3505.3865881066999,null,5.439915184979327E-11,-8.1283070552107262E-14,1.6041390438203962E-11,-3.910372470272705E-9]
[null,null,null,null,400,-5.8676438448019511E-3,1.9733871198827633,3525.4187694343977,null,400.00000000005667,-5.8676438448774255E-3,1.9733871198980206,3525.4187694306388,null,5.6672888604225591E-11,-7.5474348992798923E-14,1.5257350938213676E-11,-3.7589416024275124E-9]
[null,null,null,null,410,-5.5876716749686979E-3,1.916127412817606,3544.8640092675241,null,410.00000000005895,-5.5876716750389091E-3,1.9161274128321355,3544.8640092639189,null,5.8946625358657911E-11,-7.021119796668529E-14,1.4529488723269424E-11,-3.6052369978278875E-9]
[null,null,null,null,420,-5.327009762712916E-3,1.8615693431938254,3563.7503211055919,null,420.00000000006122,-5.3270097627783376E-3,1.8615693432076768,3563.7503211021312,null,6.1220362113090232E-11,-6.5421626449513326E-14,1.3851364499828378E-11,-3.4606273402459919E-9]
[null,null,null,null,430,-5.0839226135761294E-3,1.8095286561495896,3582.1037855902578,null,430.00000000006349,-5.0839226136372064E-3,1.8095286561628123,3582.103785586939,null,6.3494098867522553E-11,-6.1077011503929413E-14,1.3222756223285614E-11,-3.3187461667694151E-9]
[null,null,null,null,440,-4.856865418603056E-3,1.7598374761480207,3599.9487242996329,null,440.00000000006577,-4.8568654186601484E-3,1.7598374761606528,3599.9487242964483,null,6.5767835621954873E-11,-5.7092351679610687E-14,1.2632117574185031E-11,-3.1845956982579082E-9]
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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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