(12 pts) Given: You have the following RLC circuit. 10 w 2ko 200mH volt =50nF Assume the following are the initial conditions for the inductor and capacitor: it(0) = 100 UA vc(0) = 4V Find: First,...

(12 pts) Given: You have the following RLC circuit. 10 w 2ko 200mH volt =50nF Assume the following are the initial conditions for the inductor and capacitor: it(0) = 100 UA vc(0) = 4V Find: First, write the governing differential equation for vc(t). Second, determine step response of the circuit fort > 0. Hint: First determine whether the circuit is over, under-, or critically damped. This will determine the form of your solution. Solution: Answer: vc(t) = 8 - e -5,000 (4 cos(8660t) + 2.07 sin(8660+)] V