hw1_sol - EML 4312 Fall 2007 Assignment 1: Partial Fraction...

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EML 4312 Fall 2007 Assignment 1: Partial Fraction Expansion The due date for this assignment is Wednesday 9/12. 1. (50 points)Determine f ( t ) given F ( s ) for the following problems. (a) (10 points) F ( s )= s 2 +2 s +2 ( s +1)( s +2) F(s) is not a strictly proper function, so we must divide. F ( s )= s 2 +2 s +2 s 2 +3 s +2 =1 s ( s +1)( s +2) =1+ 1 ( s +1) + 2 ( s +2) F ( t )= δ ( t )+ e t 2 e 2 t (b) (10 points) F ( s )= 2 s 2 6 s +13 s 1 s 2 2 s +2 F ( s )= 2 ( s 3) 2 +2 2 s 1 ( s 1) 2 +1 2 F ( t )= e 3 t sin 2 t e t cos t (c) (10 points) F ( s )= s +10 s 2 +6 s +34 F ( s )= s +3+7 ( s +3) 2 +5 2 = s +3 ( s +3) 2 +5 2 + 7 5 5 ( s +3) 2 +5 2 F ( t )= e 3 t cos(5 t )+ 7 5 e 3 t sin(5 t ) (d) (20 points) F ( s )= 1 ( s +1) 3 ( s +2) 1 ( s +1) 3 ( s +2) = A s +1 + B ( s +1) 2 + C ( s +1) 3 + D s +2 1 ( s +1) 3 | s = 2 = A ( s +2) s +1 + B ( s +2) ( s +1) 2
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This note was uploaded on 03/18/2008 for the course EML 4312 taught by Professor Dixon during the Fall '07 term at University of Florida.

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hw1_sol - EML 4312 Fall 2007 Assignment 1: Partial Fraction...

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