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(Solved): Q2. Consider the electric circuit shown in Fig. 2. The differential equation that relates Figur ...



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Q2. Consider the electric circuit shown in Fig. 2. The differential equation that relates Figure 2: Q2 the input and output is (a). Find the characteristic equation for this circuit, and express the root(s) of the characteristic equation in terms of and . (b). Determine the zero-input response given an initial capacitor voltage of 1 volt and an initial inductor current of zero amps. That is, find given and . (c). Plot for . Does the zero-input response, which is caused solely by initial conditions, ever "die out"? (d). Determine the total response to the input . Assume an initial inductor current of , an initial capacitor voltage of , and .


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The differential equation relating the input and output is given as,




Applying Laplace transforms
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