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EECE 213 HW 2

# EECE 213 HW 2 - Matthew Thompson EECE 213 HW#2 ltr =...

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Unformatted text preview: Matthew Thompson EECE 213 HW #2 ltr = LaplaceTransform @ f_ @ t_ D , t_, s_ D : > Symbol @ ToUpperCase @ SymbolName @ f [email protected] s D Protect @ ltr D Off @ Clear:: wrsym , Remove:: rmptc D 9-31 a) In[115]:= eqn = 500 v' @ t D + 2500 v @ t D Out[115]= 2500 v @ t D + 500 v ¢ @ t D In[116]:= slnT = LaplaceTransform @ eqn, t, s D . 8 ltr < Out[116]= 2500 V @ s D + 500 H- v @ D + s V @ s DL In[117]:= slnT2 = Flatten @ Solve @ slnT, V @ s DDD Out[117]= : V @ s D fi v @ D 5 + s > In[118]:= slnT3 = slnT2 . 8 v @ D fi 100 < FullSimplify Out[118]= : V @ s D fi 100 5 + s > In[119]:= H V @ s D . slnT3 L Apart Out[119]= 100 5 + s In[120]:= InverseLaplaceTransform @ V @ s D . slnT3, s, t D Expand Out[120]= 100 ª- 5 t b) In[152]:= Clear @ "Global` * " D ; Remove @ "Global` * " D In[153]:= eqn = 5 v' @ t D + 200 v @ t D 400 HeavisideTheta @ t D Out[153]= 200 v @ t D + 5 v ¢ @ t D 400 HeavisideTheta @ t D Printed by Mathematica for Students In[154]:= slnT = LaplaceTransform @ eqn, t, s D . 8 ltr, v @ D fi H- 100 L< Out[154]= 200 V @ s D + 5 H 100 + s V @ s DL 400 s In[155]:= slnT2 = Flatten @ Solve @ slnT, V @ s DDD FullSimplify Out[155]= : V @ s D fi 2 1 s- 51 40 + s > In[156]:= H V @ s D . slnT2 L Apart Out[156]= 2 s- 102 40 + s In[157]:= InverseLaplaceTransform @ V @ s D . slnT2, s, t D Expand Out[157]= 2- 102 ª- 40 t 9-33 a) iL[0-] = 0 In[147]:= eqn = iL @ t D + 0.000825 iL' @ t D 0.0375 HeavisideTheta @ t D Out[147]= iL @ t D + 0.000825 iL ¢ @ t D 0.0375 HeavisideTheta @ t D b) In[148]:= slnT = LaplaceTransform @ eqn, t, s D . 8 ltr, iL @ D fi < Out[148]= IL @ s D + 0.000825 s IL @ s D 0.0375 s In[149]:= slnT2 = Flatten @ Solve @ slnT, IL @ s DDD FullSimplify Out[149]= : IL @ s D fi 0.0375 H 1. + 0.000825 s L s > In[150]:= H IL @ s D . slnT2 L Apart Out[150]=- 0.0000309375 1. + 0.000825 s + 0.0375 s In[151]:= InverseLaplaceTransform @ IL @ s D . slnT2, s, t D Expand Out[151]=...
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EECE 213 HW 2 - Matthew Thompson EECE 213 HW#2 ltr =...

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