"Answer the following questions for the given circuit. (10)
1. Using the Laplace transform to determine $v_2$, find the Laplace transform
expression for the input-output ratio $V_2(s)/I_g(s)$.
2. Given $R = 2500 \, \Omega$, $L = 500 \, mH$, $C = 0.5 \, \mu F$, and $i_g(t) = 30 \, mA$,
calculate $v_2(t)$."
3. (1)$V_2(s)/I_g(s) = s/[C(s^2+sR/L+1/LC)]$
(2)$V_2(s) = 6 \times 10^4/(s^2+5000s+4 \times 10^6) = 20/(s+1000)-20/(s+4000)$
$---> V_2(t) = 20(e^{-1000t} - e^{-4000t})u(t)$ [V]
