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practice_problem_set3_solution

practice_problem_set3_solution - EEL3105 Fall2011 1 f(t...

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EEL 3105 Fall 2011 Practice Problem Set 3 Solution 1. Find Laplace transform of ( ) 7 ( 4) 4 ( 2) 3sin(6 / 4) f t U t t t Here U(t) is the unit step function, (t) is the unit impulse function. Answer: We use properties of Laplace transforms and linearity to calculate F(s). 4 2 2 2 2 4 2 2 (7 ( 4)) 7 ; (4 ( 2)) 4 ; sin(6 ) cos(6 ) 18 3 3sin(6 ) 3 3 4 2 2 2( 36) 2( 36) 3 6 ( 36) 2 3 6 ( ) 7 4 . ( 36) 2 s s s s e LT U t s LT t e t t s LT t LT s s s s e s F s e s s 2. Find inverse Laplace transform for the following functions: a. F(s) = 2 2 ( 2 9) s s s s b. F(s) = 2 2 2 ( 2 9) s s e s s s Answer: Let’s start with part (a). We will break it into a partial fraction expansion of the form:
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