[13 marks] Consider a series RLC circuit, where R = 16 0, L = 2 H, C= 0.02 F, and the source voltage is v(t) = 200 sin(5t). Find the charge on the capacitor and the current in the circuit if at time zero the charge O(0) = 3 Coulombs, and the current I(0) = 0 Amperes. Hint: v(t) = Vp(t) + vz(t) +vc(t) where vp = iR; vi = La; vc and i(t) = dQ dt