Problem $2$: Consider the unity$-$feedback control system whose open$-$loop transfer function is given by:

$\backslash [$

G$($s$)=\backslash$frac$\{10\}\{$s$($s$+4)\}$

$\backslash ]$

First, compute: $($a$)$ the closed loop transfer function, and then compute: $($b$)$ rise time, $($c$)$ peak time, $($d$)$ maximum overshoot, and $($e$)$ settling time of the unit$-$step closed$-$loop system response.

Note: To get full credit, please, include all the steps of the solution process, including, any necessary diagrams or assumptions. Please, note that obtaining the correct answer using a different approach, will not be considered as a full credit solution.