Q.3 a) Determine the differential equation that relates the input x(t) to output y(t). Recall that Consider the electric circuit shown below. ic(t) = ce and v(t) = L di dt dt x(1) y(t) b) Find the...

Extracted text: Q.3 a) Determine the differential equation that relates the input x(t) to output y(t). Recall that Consider the electric circuit shown below. ic(t) = ce and v(t) = L di dt dt x(1) y(t) 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 yz-i(t) given ve(0-) = 1 V and i(0) = 0 A. [Hint: %3D The coefficient(s) in y,-(t) are independent of L and C.]