The switch in Figure has been closed for a long time and is opened at t = 0.
(a) Find the circuit differential equation in vC(t) and the initial conditions iL(0) and vC(0).
(b) The circuit parameters are L = 50 H, C = 0.25 μF, R1 = 10 kΩ, R2 = 20 kΩ, and vS = 10u (t) V. V. Use Laplace transforms and MATLAB to solve for vC(t) for t ≥ 0: