practice_problem_set3

practice_problem_set3 - EEL3105 Fall2011...

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EEL 3105 Fall 2011 Practice Problem Set 3 1. Find Laplace transform of ( ) 7 ( 4) 4 ( 2) 3sin(6 / 4) ft Ut t t  Here U(t) is the unit step function, (t) is the unit impulse function. 2. Find inverse Laplace transform for the following functions: a. F(s) = 2 2 (2 9 ) s ss s  b. F(s) = 2 2 2 9 ) s s e s 3. Consider the differential equation 2 2 51 0 38 d y dy du yu dt dt dt  Find the transfer function H(s)= () . Ys Us 4. Consider the differential equation 2 2 0 d y dy du dt dt dt Find A, B, C for a state space representation of the form . dx Ax t Bu t dt yt Cxt  5. Consider the differential equation 32 90 . dy d y dt dt dt We are given that y(t)=4e 3t is a solution to this differential equation. Find the value of .
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6. Consider the differential equation 2 2 41 6( ) . dy d y y ut dt dt  Suppose u=unit impulse function and y(0)=0, dy/dt(0)=0. Find y(t). You can use any method to solve this problem. 7. Consider the differential equation 3() () . dy y tu t dt  Suppose u(t) is the unit step function. Calculate
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practice_problem_set3 - EEL3105 Fall2011...

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