System representation $(30\%)$

$\frac{d^{2}y}{d{t}^2}+10\frac{dy}{dt}+25y=5$

$e=r-y$

$\frac{d}{dt}=2i+5e-10$

$\frac{di}{dt}=e$

$($a$)$ Sketch a signal$-$flow diagram or a block diagram of the system,

$($b$)$Identifying the component parts and determine the state space representation of the system with state

$x={\left[\begin{array}{cccc}y& y^{}& & i\end{array}\right]}^T$

and output $y.$

$($c$)$ Determine the transfer function $Y\frac{s}{R}(s).$

$5.$ System modelling $(15$

Obtain the transfer function of

$\frac{V_2(s)}{V_1(s)}$