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hw07-3723-06f - ECEN/MAE 3723 Systems I Fall 2006 Homework...

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ECEN/MAE 3723 Systems I Fall 2006 Homework Assignment #7 Problem 1 : Given an electrical circuit shown below, the voltage source E is suddenly connected by means of switch S at t = 0 . Assume that capacitor C is initially uncharged and that inductance L carries no initial current. What is the current i t ( ) for t > 0 ? Problem 2 : Derive the transfer function E s E s o i ( ) ( ) of the electrical circuit shown below. Then obtain the response e t o ( ) when the input e t i ( ) is a unit step of magnitude E i (i.e., e t E u t i i ( ) ( ) = ). Assume that the initial charge in the capacitor is zero. Problem 3 : Derive the transfer function E s E s o i ( ) ( ) of the electrical circuit shown below. Then obtain the response e t o ( ) when the input e t i ( ) is a unit step of magnitude E i (i.e., e t E u t i i ( ) ( ) = ). Assume that the initial charge in the capacitor is zero. Problem 4 : Consider the mechanical system shown below, where 1 1 = k N/m, 2 2 = k N/m, 5 0 1 . = b N-s/m, and 1 2 = b N-s/m. Obtain the response ) ( t x o when ) ( t x i is a unit-step displacement input.
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