Problem 9 (12 pts.): For the circuit shown below the input is $v_1(t)$ and the output is $v_2(t)$.
a) (5 pts.) Determine the expression of the transfer function $G(s) = \frac{V_2(s)}{V_1(s)}$
b) (3 pts.) Determine the natural frequency $\omega_n$ and the damping ration $\zeta$ and decide if the circuit is
underdamped, critically damped or overdamped.
c) (4 pts.) Calculate $v_2(t)$ if $v_1(t) = 2V$, for $t > 0.$
