me352_hw3 - G(s) first, and then use the Laplace transform...

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1 ME 352 System Dynamics and Control Homework #3 Due: Friday 25.03.2010 [1]. Find the free response and the forced (step) response of the following models (i.e., solve the differential equations by using the Laplace transform). If the solution is oscillatory, it should be expressed in the form of trigonometric functions. (a) 1 ) 0 ( , 0 ) 0 ( , 2 8 4 = = = + + x x x x x (b) 1 ) 0 ( , 0 ) 0 ( , 2 12 8 = = = + + x x x x x (c) 1 ) 0 ( , 0 ) 0 ( , 2 4 4 = = = + + x x x x x [2]. Find the Laplace transform of the following functions. (a) ) ( 1 ) 2 sin ( ) ( 2 t e t t t g t - + = (b) ) ( 1 ) 2 sin( 2 ) ( 2 t t e t g t - = [3]. Find the inverse Laplace transforms of the following functions. Perform partial-fraction expansion on
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Unformatted text preview: G(s) first, and then use the Laplace transform table. (a) ) 3 ( ) 1 ( 10 ) ( 2 + + = s s s G (b) ) 2 ( ) 1 ( 2 ) ( 2 + + + = s s s s s G [4]. Find the transfer function ) ( ) ( 1 s U s X for the following block diagrams. (a) 1 X1(s) 1 s+5 Transfer Fcn1 1 s+2 Transfer Fcn 20 Gain2 3 Gain1 5 Gain 1 U(s) (b) 1 X1(s) 1 s+5 Transfer Fcn1 1 s+2 Transfer Fcn 20 Gain2 3 Gain1 1 U(s)...
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