Hw03-3723-06f - ECEN/MAE 3723 Systems I Fall 2006 Homework Assignment#3 Problem 1 Find the one-sided Laplace transform of each of the following

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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) et t 2 0 2 sin ω , b) () at n , c) d dt t sin , d) ) sin( θ + ϖ t , e) + dt t ) cos( θ ω , f) ) 1 ( sin 2 t u te t , and g) 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 44 2 ss ++ , b) 2 61 3 2 , c) 23 2 32 2 2 , d) s 3 3 1 + , e) es s + + 1 2 2 , f) 1 4 + e s , g) se s 2 2 11 ( ) , h) ( ) sss 22 46 6 21 0 . i) c s e b s e as as 2 1 −− j) c b s c a s + + + + ln .
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Problem 4 : A continuous-time signal ) ( 3 sin ) ( 2 t tu e t x t = has the Laplace transform ) ( s X . Determine the inverse Laplace transform of ) ( s V , ) ( t v , where ) ( 2 ) ( 5 5 s X e e s V s s + = . Problem 5 : Solve the following differential equations (to find x ( t )) using Laplace transform and Inverse Laplace transform: a) dxt dt xt 2 2 40 () += , where x 01 = and = x , b) dt dx t dt t 2 2 2 2 , where x 02 = and = x , c) dt t
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This note was uploaded on 12/26/2010 for the course ECEN 3723 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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Hw03-3723-06f - ECEN/MAE 3723 Systems I Fall 2006 Homework Assignment#3 Problem 1 Find the one-sided Laplace transform of each of the following

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