Problem $1$:

For the circuit shown in the below Figure:

$L=2\mathrm{.}5H,R=15,C=0\mathrm{.}1F$

$($a$)$ The circuit's natural frequency ${}_n.$

$($b$)$ The damping ratio, $.$

$($c$)$ The percent overshoot in the circuit's unit step response.

$($d$)$ The circuit's settling time for a unit step input.

$($e$)$ The peak time of the circuit's unit step response.

$($f$)$ The location of the poles of the system.