EECE_213_2011_Spring_Exam2

EECE_213_2011_Spring_Exam2 - Problem 1 Clear @...

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Unformatted text preview: Problem 1 Clear @ "Global` * " D Assume the following T[s] and v1[t]: T @ s_ D : = 2000 H s + 2000 L H s + 1000 L H s + 4000 L v1 @ t_ D : = I 20 + 15 ª- 5000 t M If V2[s] = T[s] V1[s], Identify Forced Poles and Natural Poles? V1 @ s_ D : = LaplaceTransform @ v1 @ t D , t, s D Together V2 @ s_ D : = T @ s D V1 @ s D V1 @ s D 5 H 20 000 + 7 s L s H 5000 + s L V2 @ s D 10 000 H 2000 + s L H 20 000 + 7 s L s H 1000 + s L H 4000 + s L H 5000 + s L Apart @ V2 @ s DD 20 s- 65 6 H 1000 + s L + 40 3 H 4000 + s L- 45 2 H 5000 + s L Solve @ Denominator @ V2 @ s DD D Flatten 8 s fi - 5000, s fi - 4000, s fi - 1000, s fi < Force poles 0 and -5000. Natural poles -4000 and -1000 find v2[t]: v2 @ t_ D = InverseLaplaceTransform @ V2 @ s D , s, t D 10 000 1 500- 9 ª- 5000 t 4000 + ª- 4000 t 750- 13 ª- 1000 t 12 000 sln = Expand @ v2 @ t DD 20- 45 ª- 5000 t 2 + 40 ª- 4000 t 3- 65 ª- 1000 t 6 Printed by Mathematica for Students Problem 2 Identify Forced Response and Natural Response? Forced response is associated with forced poles, those of V1[s]. Natural response is associated with the other poles. v2forced @ t_ D = 20- 45 ª- 5000 t 2 20- 45 ª- 5000 t 2 v2natural @ t_ D = 40 ª- 4000 t 3- 65 ª- 1000 t 6 40 ª- 4000 t 3- 65 ª- 1000 t 6 Problem 3 Clear @ "Global` * " D H @ s_ D : = s + 2000 s + 1000 x @ t_ D : = 5 ª- 1000 t Note that the HeavisideTheta or unit step function is superfluous. X @ s_ D = LaplaceTransform @ x @ t D , t, s D 5 1000 + s Y @ s_ D = H @ s D X @ s D 5 H 2000 + s L H 1000 + s L 2 y @ t_ D = InverseLaplaceTransform @ Y @ s D , s, t D 5 ª- 1000 t H 1 + 1000 t L Problem 4 The oberved step response of a circuit is given by this function. Find the impulse response and the transfer function.The oberved step response of a circuit is given by this function....
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This note was uploaded on 02/08/2012 for the course EECE 213 taught by Professor Mendenhall during the Spring '11 term at Vanderbilt.

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EECE_213_2011_Spring_Exam2 - Problem 1 Clear @...

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