Q$.$ The voltage source in the circuit in Example $13\mathrm{.}9$ is changed to a unit impulse; that is$,v_g=(t).$

a$)$ How much energy does the impulsive voltage source store in the capacitor?

b$)$ How much energy does it store in the inductor?

c$)$ Use the transfer function to find $v_o(t).$

d$)$ Show that the response found in $($c$)$ is identical to the response generated by first charging the capacitor to $1000$ V and then releasing the charge to the circuit, as shown in Fig. P$13\mathrm{.}84.$

Figure $13\mathrm{.}31$ The circuit for Example $13\mathrm{.}9.$