For a system described by the transfer function

H$($s$)=3$s $+2$

$3$s$2+7$s $+2,$

$(4$a$)$ Derive the spectrum of H$($$).$

$(4$b$)$ Find the system response to the input u$($t$),$ where u$($t$)$ is the unit step

function.

$(4$c$)$ Find the system response to the sinusoidal input cos$(3$t $45$o$)$u$($t$),$ where

u$($t$)$ is the unit step function.

$(4$d$)$ Find the system response to the sinusoidal input sin$(2$t $+60$o$)$u$($t$),$ where

u$($t$)$ is the unit step function