P1. (10 points) The LC circuit shown in Figure P1 is subjected to input voltage Vin that is suddenly applied at time, t = 0. The voltage v(t) satisfies the equation 1, a second order differential equation. LC dv(t) dx +v(t) = Vin Where: v(t) = the velocity at time t L = inductance = 100 mH C Vin Initial conditions: (1) = capacitance = 40 F source voltage = 10.0 V (applied when t > 0) v(0) = 0 and (0) = 0 Determine the resulting equation for v(t). Clearly show all steps. L moooo Figure P1: The RC circuit for problem P1. The capacitance is 40 uF and the inductance is 100 mH. v(t)