QUESTION $2$

$($a$)$ Determine the output $C$ due to inputs $R$ and $U$ using the superposition method for the diagram shown in Figure Q$2$a$.$

$(10$ marks$)$

$($b$)$ Draw the block diagram for the following system represented by equation below:

$($i$),x_3=a_1{x}_1+a_2{x}_2-5.$

$(3$ marks$)$

$($ii$),x_2=a_1(\frac{d{x}_1}{dt})+\frac{1}{b}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}_{1}dt$

$(3$ marks$)$

$($iii$),x_3=a_1\frac{d^2{x}_2}{d{t}^2}+3\frac{d{x}_1}{dt}-b{x}_1$

$(4$ marks$)$

$2$