Consider the LC circuit of Problem 8.2. Parts of this problem are repeated from Problem...

Consider the LC circuit of Problem 8.2. Parts of this problem are repeated from Problem 8.2. Use those results if available.

(a) Write the state equations of the circuit, with the state variables equal to the current i(t) and the capacitor voltage v_c(t), and the output equal to i(t).

(b) Use the results of part (a) to find the circuit transfer function.

(c) Use the s-plane impedance approach to verify the transfer function of part (b). Recall that for the impedance approach, the impedance of the inductance is sL and of the capacitance is 1/(sC).