In the circuit shown below, the switch on the left has been kept open for a long time before closing at t = 0. Similary, the switch on the right has been kept closed for a long time before opening at t = 0. a) Find the initial values of the capacitor voltage, vc (0), and the inductor current, i, (0-). b) For t > 0, derive the differential equation for the circuit and write the characteristic equation for the capacitor voltage, vc(t). Find the roots of the characteristic equation. c) Find ve(t) and i, (t) fort 0. d) Is the capacitor voltage response overdamped, underdamped or critically damped? Explain. (=2.10-4 C=5-10-7 JA() t=0 1-11 ww 0.5 F HH + UC 40 va 0000 iL t=0 x. 0.2 mH va 5A 1. DI