Q$1$: Find the transfer function of a second $-$order system that yields a $12\mathrm{.}3\%$ overshoot and a settling time of $1$ second.

$$ Q$2$: A second$-$order system has the closed$-$loop transfer function.

$T(s)=\frac{Y(s)}{R(s)}=\frac{{}_n^2}{s^2+2{}_{n}s+{}_n^2}=\frac{7}{s^2+3\mathrm{.}175s+7}.$

Determine the percent overshoot, the time to peak, and the settling time of the unit step response, $R(s)=\frac{1}{s}.$