QUESTION $2$

Given the transfer function below:

$G(s)=\frac{Y(s)}{U(s)}=\frac{10}{(5s+1)(3s+1)}$

What is $y(t)$ for the subsequent inputs:

$2\mathrm{.}1$ Step input of height $M$

$2\mathrm{.}2$ Unit impulse input $(t)$

$2\mathrm{.}3sin(t)$

$2\mathrm{.}4$ Unit rectangular pulse, where $h=1)$

$f(t)=\{\begin{array}{cc}0,& t<mn\; id="EditorElement\_172008">0</mn>\\ h,& 0t=t_w\end{array}$

$[33$ Marks$]$