LC-Circuit: Consider the series LC-circuit shown in Fig. 4. 1. 11, in which, at t = 0, the current is 5 amps and there is no charge on the capacitor. Voltage V0 is turned off at r = 0.

(a) Before carrying out the mathematical analysis, describe what you think will happen to the charge on the capacitor.
(b) For t > 0, use Kirchoff's voltage law to determine the sum of the voltage drops around the circuit. Set it equal to zero to obtain a second-order differential equation involving L, Q, Q, and C. What are the initial conditions?
(c) Solve the IVP in (b) for the charge Q on the capacitor. Does your result agree with pan (a)?
(d) Obtain an explicit solution for L = 10 henries and C = 10-3 farads.

C- 10 farads v(n) =1% for ' < 0 0 for 20 L- 10 henries FIGURE 4.111 An LC-circuit (Problem 58).