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hw03-3723-06f - ECEN/MAE 3723 Systems I Fall 2006 Homework...

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ECEN/MAE 3723 Systems I Fall 2006 Homework Assignment #3 Problem 1 : Find the one-sided Laplace transform of each of the following functions: a) e t t 2 0 2 sin ω , b) ( ) at n , c) ( ) d dt e t t sin , d) ) sin( θ + ϖ t , e) + dt t ) cos( θ ω , f) ) 1 ( sin 2 t u te t , and g) λ λ λ d t u ) ( 0 . Problem 2 : A continuous-time signal x t ( ) has the Laplace transform 7 5 1 2 + + + = s s s s X ) ( , determine the Laplace transforms of ) ( s V for t sin t x t v 2 ) ( ) ( = . Problem 3 : Find the inverse Laplace transform of a) 1 4 4 2 s s + + , b) 2 6 13 2 s s + + , c) 2 3 2 3 2 2 2 s s s s + + + + , d) ( ) s s s 3 3 3 2 1 + + + , e) ( ) e s s s s + + 1 2 2 , f) 1 3 2 4 3 2 + e s s s , g) se s s s + + 2 2 1 1 ( )( ) , h) ( )( ) s s s s s s s 3 2 2 2 4 6 6 2 10 4 4 + + + + + + . i) c s e b s e as as 2 1 ( ) j) c b s c a s + + + + ln .
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