Problem $3$:

Consider the closed$-$loop system shown below:

Where:

$G(s)=\frac{k}{(s+2)(s+3)}$

$(k$ is a positive or negative constant parameter$)$

$($a$)$ Compute the Transfer Function of the closed$-$loop system, $T(s)=\frac{Y(s)}{R(s)}$

$($b$)$ Calculate the allowed values of $k$ for a stable system.