{"text_format":"3","workbook":"xlsx","n_sheets":2,"sheets":["RLC Circuit","Sheet2"],"not_rendered":{"charts":2,"images":5,"defined_names":31,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"RLC Circuit","index":0,"n_rows":44,"n_cols":10,"rows_kept":44}
["              Modeling The RLC Circuit"]
[]
[null,"This DIGMath module lets you investigate "]
[null,"   the behavior of an RLC electrical circuit:"]
[null,"   how the current I in a circuit depends on"]
[null,"           the Resistance R of a resistor, "]
[null,"    the  Inductance L of an inductor, and "]
[null,"     and the Capacitance C of a capacitor."]
[]
["What is the initial current I0 (0 to 200 milliamps)?"]
[null,null,{"$f":"10*D11","v":60},6]
[]
[]
["What is the inductance L (100 - 1000 mh)?"]
[null,null,{"$f":"D15*50","v":400},8,7]
[]
["What is the resistance R (0 - 2000 ohms)?"]
[null,null,{"$f":"D18*10","v":1090},109]
[]
["What is the capacitance C (1 - 20 mF)?",{"$nulls":6},"Now trace a point along the curve for the current I."]
[null,null,{"$f":"D21","v":4},4,{"$nulls":5},431]
[{"$nulls":7},"t =",{"$f":"J21*dtt","v":43.1},"seconds"]
["This combination produces",null,null,{"$f":"IF(case=1,\"critical damping\",IF(case=2,\"over-damping\",\"under-damping\"))","v":"under-damping"},{"$nulls":3},"I =",{"$f":"LOOKUP(I$22+0.001,Sheet2!C3:C1003,Sheet2!G3:G1003)","v":{"v":-21.543142608406644,"d":"-21.54"}},"milliamps above/below the equilibrium level"]
["  for the solution of the D.E.",null,null,{"$f":"TEXT(a00,\"0\")&\" I''  + \"&TEXT(kk,\"0\")&\" I' + \"&TEXT(1/cc,\"0.00\") &\" I = 0\"","v":"400 I''  + 1090 I' + 0.25 I = 0"}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2"]
[null,"   Item 3"]
[null,"   Item 4"]
[null,"   Item 5"]
[null,"   Item 6"]
[null,"   Item 7"]
[]
[]
["To access/download all the DIGMath Apps for Differential Equations"]
["     Click this link:",null,"https://we-dig-math.org/dynamic-differential-equations.html"]
[]
["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":1003,"n_cols":9,"rows_kept":1003}
[null,null,"t","y1","y2","y3","y","v"]
[]
[null,null,0,{"$f":"(B$20+B$21*tt)*EXP(-omega0*tt)","v":60},{"$f":"B$24*EXP(gamma2*tt)+B$25*EXP(gamma2*tt)","v":{"$error":"#NUM!"}},{"$f":"EXP(-cc/2/mm*tt)*(B$29*COS(SQRT(-Disc)/2/mm*tt)+B$30*SIN(SQRT(-Disc)/2/mm*tt))","v":60},{"$f":"IF(case=1,D3,IF(case=2,E3,F3))","v":60},null,0]
["sqrt(k/m) =",{"$f":"SQRT(kk/mm)","v":1.6507574019219178},{"$f":"C3+dtt","v":0.1},50.87135889355305,{"$error":"#NUM!"},59.1566355323907,59.1566355323907,null,0]
[null,null,0.2,43.13158588582659,{"$error":"#NUM!"},56.706542246140266,56.706542246140266,null,0]
[null,null,0.30000000000000004,36.569373016015334,{"$error":"#NUM!"},52.7179069457636,52.7179069457636,null,0]
["gamma =",{"$f":"1/cc/2/SQRT(mm*kk)","v":1.893070415048071E-4},0.4,31.00556156267359,{"$error":"#NUM!"},47.30065790717449,47.30065790717449,null,0]
["disc=",{"$f":"1/cc^2-4*mm*kk","v":-1743999.9375},0.5,26.288250729842925,{"$error":"#NUM!"},40.60343587440777,40.60343587440777,null,0]
[null,null,0.6,22.28865051721489,{"$error":"#NUM!"},32.80951607892855,32.80951607892855,null,0]
["v0 =",0,0.7,18.897565551199886,{"$error":"#NUM!"},24.131793148430944,24.131793148430944,null,0]
[null,null,0.7999999999999999,16.022413879991394,{"$error":"#NUM!"},14.806966126039965,14.806966126039965,null,0]
["delta t = ",0.1,0.8999999999999999,13.584699341067507,{"$error":"#NUM!"},5.08908242054561,5.08908242054561,null,0]
[null,null,0.9999999999999999,11.517868492808006,{"$error":"#NUM!"},-4.757383229500737,-4.757383229500737,null,0]
["gamma1 =",{"$f":"(-kk+SQRT(1/cc^2-4*mm*kk))/2/mm","v":{"$error":"#NUM!"}},1.0999999999999999,9.765493601106341,{"$error":"#NUM!"},-14.464726235070458,-14.464726235070458,null,0]
["gamma2 =",{"$f":"(-kk-SQRT(1/cc^2-4*mm*kk))/2/mm","v":{"$error":"#NUM!"}},1.2,8.27973207366718,{"$error":"#NUM!"},-23.769290212711372,-23.769290212711372,null,0]
[null,null,1.3,7.020020282133965,{"$error":"#NUM!"},-32.4186277568679,-32.4186277568679,null,0]
[null,null,1.4000000000000001,5.951966111345282,{"$error":"#NUM!"},-40.17834945289227,-40.17834945289227,null,0]
[null,null,1.5000000000000002,5.046410000580289,{"$error":"#NUM!"},-46.838475321557546,-46.838475321557546,null,0]
["1. Critical damping",null,1.6000000000000003,4.278628841748347,{"$error":"#NUM!"},-52.219116592940566,-52.219116592940566,null,0]
["A =",{"$f":"yy0","v":60},1.7000000000000004,3.6276609996960154,{"$error":"#NUM!"},-56.17533407774785,-56.17533407774785,null,0]
["B =",{"$f":"v0+1/cc/2/mm*yy0","v":0.01875},1.8000000000000005,3.075734026628073,{"$error":"#NUM!"},-58.60104193363983,-58.60104193363983,null,0]
[null,null,1.9000000000000006,2.6077794463491575,{"$error":"#NUM!"},-59.43185169647923,-59.43185169647923,null,0]
["2. Over-damped",null,2.0000000000000004,2.2110213611751313,{"$error":"#NUM!"},-58.6467803496309,-58.6467803496309,null,0]
["A =",{"$f":"(v0-gamma2*yy0)/(gamma1-gamma2)","v":{"$error":"#NUM!"}},2.1000000000000005,1.8746276498377288,{"$error":"#NUM!"},-56.26877715020765,-56.26877715020765,null,0]
["B =",{"$f":"yy0-B24","v":{"$error":"#NUM!"}},2.2000000000000006,1.589414233538201,{"$error":"#NUM!"},-52.364056076498564,-52.364056076498564,null,0]
[null,null,2.3000000000000007,1.3475943361492952,{"$error":"#NUM!"},-47.04025323099217,-47.04025323099217,null,0]
[null,null,2.400000000000001,1.1425658929756346,{"$error":"#NUM!"},-40.44346044571899,-40.44346044571899,null,0]
["3. Under-damped",null,2.500000000000001,0.9687313039980241,{"$error":"#NUM!"},-32.75421682443212,-32.75421682443212,null,0]
["A =",{"$f":"yy0","v":60},2.600000000000001,0.8213446105823061,{"$error":"#NUM!"},-24.18256819234478,-24.18256819234478,null,0]
["B =",{"$f":"1/B32*(gamma*omega0*yy0+v0)","v":0.011358422693815207},2.700000000000001,0.6963819233369682,{"$error":"#NUM!"},-14.96232964368607,-14.96232964368607,null,0]
[null,null,2.800000000000001,0.5904315635965514,{"$error":"#NUM!"},-5.34470789789653,-5.34470789789653,null,0]
["omegaD =",{"$f":"omega0*SQRT(1-gamma^2)","v":1.6507573723426925},2.9000000000000012,0.500600919220785,{"$error":"#NUM!"},4.408542584251084,4.408542584251084,null,0]
["gamma =",null,3.0000000000000013,0.4244374717264417,{"$error":"#NUM!"},14.032243277189698,14.032243277189698,null,0]
[null,null,3.1000000000000014,0.359861838668511,{"$error":"#NUM!"},23.265001195373454,23.265001195373454,null,0]
[null,null,3.2000000000000015,0.3051110032224638,{"$error":"#NUM!"},31.856308420668903,31.856308420668903,null,0]
["case =",{"$f":"IF(Disc<0,3,IF(Disc>0,2,1))","v":3},3.3000000000000016,0.25869018104595953,{"$error":"#NUM!"},39.573338733866095,39.573338733866095,null,0]
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