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[null,"            The Pendulum and"]
[null,"       Simple Harmonic Motion"]
[]
[null,"        This DIGMath program lets you "]
[null," investigate the motion of a simple pendulum"]
[null," based on the 2nd order differential equation"]
[null,null,"        q'' =g/L sin(q)"]
[null,"         with initial condition q(0) = q0"]
[null,"      extending from t = 0  to  t = tMax."]
[]
["What is the length L (in feet, 0.5 - 10) of the pendulum?"]
[null,null,{"$f":"E12/10","v":5.4},null,54]
[]
["What is the initial angle q0 ( -6° to +6°)?"]
[null,null,{"$f":"E15/2-6","v":5},null,22]
[]
[{"$nulls":7},"Trace a point along the path of the pendulum"]
["To what value of t should the solution extend?",{"$nulls":6},"     t =",{"$f":"K18*dt","v":10.96},null,274]
[null,null,"   tMax =",20,{"$nulls":4},"     q =",{"$f":"LOOKUP(t0+0.001,Sheet2!C3:C503,Sheet2!D3:D503)","v":{"v":0.06562804057482095,"d":"0.07"}},"radians =",{"$f":"180/PI()*J19","v":{"v":3.7602097426505616,"d":"3.76"}},"°"]
[null,null,{"$f":"IF(b<=0,\"That must be larger than 0\",\"\")","v":""},{"$nulls":5},"    x =",{"$f":"LOOKUP(t0+0.001,Sheet2!C3:C503,Sheet2!E3:E503)","v":{"v":0.3541370775640254,"d":"0.35"}}]
[{"$nulls":8},"   y =",{"$f":"LOOKUP(t0+0.001,Sheet2!C3:C503,Sheet2!F3:F503)","v":{"v":-5.388375166067635,"d":"-5.39"}}]
[]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2"]
[null,"   Item 3"]
[null,"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Sheet2","index":1,"n_rows":503,"n_cols":9,"rows_kept":503}
[{"$nulls":4},"Taylor - linear"]
[null,null,"t","q(t)","x","y","Plotting q","Plotting x","Plotting y"]
[null,null,{"$f":"0","v":0},{"$f":"qq0","v":0.08726646259971647},{"$f":"L*SIN(D3)","v":0.4706410108373541},{"$f":"-L*COS(D3)","v":-5.379451369695427},{"$f":"IF(ABS(qq0)<=0.10473,D3,#REF!)","v":0.08726646259971647},{"$f":"IF(ABS(qq0)<0.1,E3,#REF!)","v":0.4706410108373541},{"$f":"IF(ABS(qq0)<0.1,F3,#REF!)","v":-5.379451369695427}]
["delta q = ",{"$f":"b/2/PI()/SQRT(L/g)*qq0/500","v":1.3524013765559657E-3},{"$f":"C3+dt","v":0.04},{"$f":"IF(qq0>0,qq0-dq,qq0+dq)","v":0.0859140612231605},0.46336540521890174,-5.380082945573082,{"$f":"IF(ABS(qq0)<=0.10473,D4,#REF!)","v":0.0859140612231605},{"$f":"IF(ABS(qq0)<=0.10473,E4,#REF!)","v":0.46336540521890174},{"$f":"IF(ABS(qq0)<=0.10473,F4,#REF!)","v":-5.380082945573082}]
[null,null,0.08,{"$f":"IF(qq0>0,    IF(AND(D4>D3,D4+dq>qq0), D4-dq,    IF( AND(D4>D3, D4+dq<=qq0), D4+dq,\n         IF(AND(D4<D3,D4-dq<-qq0),D4+dq,   D4 - dq)) ),  IF(AND(D4>D3,  D4+dq > -qq0), D4-dq,\n                   IF(  AND(D4>D3, D4+dq< -qq0), D4+dq,   IF(AND(D4<D3,D4-dq<=qq0),  D4+dq,    D4-dq ) ) ) )","v":0.08456165984660453},0.4560889521101255,-5.38070468133711,{"$f":"IF(ABS(qq0)<=0.10473,D5,#REF!)","v":0.08456165984660453},{"$f":"IF(ABS(qq0)<=0.10473,E5,#REF!)","v":0.4560889521101255},{"$f":"IF(ABS(qq0)<=0.10473,F5,#REF!)","v":-5.38070468133711}]
["delta t =",{"$f":"(b)/500","v":0.04},0.12,0.08320925847004856,0.44881166481957946,-5.381316575850363,{"$f":"IF(ABS(qq0)<=0.10473,D6,#REF!)","v":0.08320925847004856},{"$f":"IF(ABS(qq0)<=0.10473,E6,#REF!)","v":0.44881166481957946},{"$f":"IF(ABS(qq0)<=0.10473,F6,#REF!)","v":-5.381316575850363}]
[null,null,0.16,0.0818568570934926,0.4415335566573436,-5.381918627993693,{"$f":"IF(ABS(qq0)<=0.10473,D7,#REF!)","v":0.0818568570934926},{"$f":"IF(ABS(qq0)<=0.10473,E7,#REF!)","v":0.4415335566573436},{"$f":"IF(ABS(qq0)<=0.10473,F7,#REF!)","v":-5.381918627993693}]
["initial angle in radians =",null,0.2,0.08050445571693662,0.43425464093499927,-5.382510836665953,{"$f":"IF(ABS(qq0)<=0.10473,D8,#REF!)","v":0.08050445571693662},{"$f":"IF(ABS(qq0)<=0.10473,E8,#REF!)","v":0.43425464093499927},{"$f":"IF(ABS(qq0)<=0.10473,F8,#REF!)","v":-5.382510836665953}]
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["xMin =",{"$f":"x0","v":1},0.36,0.07509485021071274,0.4051311687273454,-5.384781215251518,{"$f":"IF(ABS(qq0)<=0.10473,D12,#REF!)","v":0.07509485021071274},{"$f":"IF(ABS(qq0)<=0.10473,E12,#REF!)","v":0.4051311687273454},{"$f":"IF(ABS(qq0)<=0.10473,F12,#REF!)","v":-5.384781215251518}]
["xMin =",1,0.39999999999999997,0.07374244883415677,0.3978484149290204,-5.385324190681418,{"$f":"IF(ABS(qq0)<=0.10473,D13,#REF!)","v":0.07374244883415677},{"$f":"IF(ABS(qq0)<=0.10473,E13,#REF!)","v":0.3978484149290204},{"$f":"IF(ABS(qq0)<=0.10473,F13,#REF!)","v":-5.385324190681418}]
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["g =",32,0.4799999999999999,0.07103764608104483,0.3832807376724115,-5.386380591466713,{"$f":"IF(ABS(qq0)<=0.10473,D15,#REF!)","v":0.07103764608104483},{"$f":"IF(ABS(qq0)<=0.10473,E15,#REF!)","v":0.3832807376724115},{"$f":"IF(ABS(qq0)<=0.10473,F15,#REF!)","v":-5.386380591466713}]
[null,null,0.5199999999999999,0.06968524470448886,0.375995840858252,-5.386894014889963,{"$f":"IF(ABS(qq0)<=0.10473,D16,#REF!)","v":0.06968524470448886},{"$f":"IF(ABS(qq0)<=0.10473,E16,#REF!)","v":0.375995840858252},{"$f":"IF(ABS(qq0)<=0.10473,F16,#REF!)","v":-5.386894014889963}]
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["Pendulum",null,0.6,0.06698044195137692,0.3614239974781869,-5.387891303102438,{"$f":"IF(ABS(qq0)<=0.10473,D18,#REF!)","v":0.06698044195137692},{"$f":"IF(ABS(qq0)<=0.10473,E18,#REF!)","v":0.3614239974781869},{"$f":"IF(ABS(qq0)<=0.10473,F18,#REF!)","v":-5.387891303102438}]
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