HW1 solution

# HW1 solution - EML4312 Spring 2011 HOMEWORK 1 SOLUTION...

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HOMEWORK 1 SOLUTION Partial Fraction Expansion The due date for this assignment is Friday 1/21. 1. Determine the inverse Laplace transform for the following problems (80points): (a) (10 points) F ( s ) = s 2 + 2 ( s + 1)( s 2 + 4) ; s 2 + 2 ( s + 1)( s 2 + 4) = A s + 1 + Bs s 2 + 4 + C s 2 + 4 ; Hence, A ( s 2 + 4) + Bs ( s + 1) + C ( s + 1) = s 2 + 2 with 8 s [ A ( s 2 + 4) + Bs ( s + 1) + C ( s + 1)] j s = 1 = ( s 2 + 2) j s = 1 ! 5 A = 3 ! A = 3 5 [ A ( s 2 + 4) + Bs ( s + 1) + C ( s + 1)] j s =0 = ( s 2 + 2) j s =0 ! 4 A + C = 2 ! C = 2 5 [ A ( s 2 + 4) + Bs ( s + 1) + C ( s + 1)] j s =1 = ( s 2 + 2) j s =1 ! 5 A + 2 B + 2 C = 3 ! B = 2 5 F ( s ) = 3 5 1 s + 1 + 2 5 s s 2 + 2 2 1 5 2 s 2 + 2 2 ! f ( t ) = 3 5 e t + 2 5 cos(2 t ) 1 5 sin(2 t ) : (b) (10 points) F ( s ) = s ( s + 2)( s + 5) = A s + 2 + B s + 5 ! A ( s + 5) + B ( s + 2) = s with 8 s [ A ( s + 5) + B ( s + 2)] j s = 2 = s j s = 2 ! 3 A = 2 ! A = 2 3 [ A ( s + 5) + B ( s + 2)] j s

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## This note was uploaded on 09/05/2011 for the course EML 4312 taught by Professor Dixon during the Spring '07 term at University of Florida.

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HW1 solution - EML4312 Spring 2011 HOMEWORK 1 SOLUTION...

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