Consider the system shown in Fig. $1,$ where $R=100,L=10mH,$ and $C=62\mathrm{.}5F.$

Figure $1$: System for Question $2$

$($a$)$ Determine a differential equation relating the input $x(t)$ and output $y(t).$

$($b$)$ Determine the impulse response of the system.

$($c$)$ Sketch the Bode plot of the frequency response.