Question B$2[15$ Marks$]$

Figure B$2$: Electrical circuit

$($i$)$ Find the system model for the system shown in Fig.B$2.$ using time domain methods. $[4$ marks $]$

$($ii$)$ Assuming that

$Dy(t)+2y(t)=x(t)$

determine the system response. Use the impulse matching method and consider an input of

$x(t)=sin(t)u(t)$

$[6$marks$]$

Together with initial conditions: $v_c(0^{-})=1V$

: $sin(x)=cos(90-x).$ Use angles in degress.

$($iii$)$ Determine the natural response and the forced response of the system.

$[2$ marks$]$

$($iv$)$ Is the system input an energy signal? Explain.

$[3$ marks$]$