HW 4 ans - ELE232 Electrical Fundamentals II 26JAN2007...

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ELE232 – Electrical Fundamentals II – 26JAN2007 Homework # 4 Answers – Due Friday, 22FEB2007 Problem 1 : (a) Do a partial fraction expansion on F(s) = 2 (s + 2 ) s(s + 1 )(s + 2 ) . (b) Determine the time function f(t) that corresponds to the Laplace Transform F(s) above. (c) Based upon the f(t) you found above, what is its value at t = 0 ? Compare that value with the one predicted by the initial value theorem that says f( 0 ) = lim s !" sF(s) ( ) . (d) Based upon the f(t) you found above, what is its value at t = ? Compare that value with the one predicted by the final value theorem that says f( ! ) = lim s " 0 sF(s) ( ) . (a) 2 1 s(s + 1 ) = A s + B s + 1 . A = 2, B = - 2 . (b) f(t) = 2 ( 1 ! e ! t )u(t) (c) If f( 0 ) = lim s !" sF(s) ( ) , then f( 0 ) = lim s !" s 2 s(s + 1 ) # $ % ( = lim s !" 2 (s + 1 ) # $ % ( = 0 and that agrees with (b) . (d) f( ! ) = lim s " 0 s 2 s(s + 1 ) # $ % ( = lim s " 0 2 (s + 1 ) # $ % ( = 2 and that agrees with (b) . Problem 2 :
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This note was uploaded on 05/02/2008 for the course ELE 232 taught by Professor Phelps during the Spring '08 term at Syracuse.

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HW 4 ans - ELE232 Electrical Fundamentals II 26JAN2007...

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