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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Consider the electric circuit shown in Fig. P2-33.
(a) Determine the differential equation that relates the input x(t) to output y (t). Recall

(b) Find the characteristic equation for this circuit, and express the root(s) of the characteristic equation in terms of L and C.
(c) Determine the zero-input response given an initial capacitor voltage of one volt and an initial inductor current of zero amps. That is, find y0(t) given vc (O) = I V and ii(O) = 0 A. [Hint: The coefficient(s) in Yo(t) are independent of L and C.]
(d) Plot Yo(t) for t :::: 0. Does the zero-input response, which is caused solely by initial conditions, ever "die" out?
(e) Determine the total response y(t) to the input x(t) = e-'u(t). Assume an initial inductor current of ii (Q-) = 0 A, a

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