Q$\mathrm{.}1)$ An SISO second order process is described by the following equation:

$y^{}(t)+2{}_n{y}^{}(t)+{}_n^{2}y(t)={}_n^{2}u(t)$

where $$ denotes damping factor, ${}_n$ natural frequency, $y(t)$ the output, and $u(t)$ the input. Assume zero initial conditions.

$($a$)$ Implement the process provided in Equation $(1)$ in Simulink.

$($b$)$ In Simulink, assuming ${}_n=1,$ investigate and discuss the step responses for $=0,0\mathrm{.}2,0\mathrm{.}5,0\mathrm{.}8,1\mathrm{.}0,2\mathrm{.}0,$ and $10\mathrm{.}0.$

$($c$)$ In Simulink, assuming $=0\mathrm{.}5,$ investigate and discuss the step responses for ${}_n=0\mathrm{.}1,1,5,$ and $10.$