The switch in Figure P9–50 has been open for a long time and is closed at t ¼ 0. The circuit parameters are R ¼ 500 V, L ¼ 2.5 H, C ¼ 2.5 mF, and VA ¼ 50 V.

(a) Find the circuit differential equation in vC(t) and the initial conditions iL(0) and vC(0).

(b) Use Laplace transforms to solve for vC(t) for t  0.