If a network is found to have the transfer function

$$

$($

$$

$)$

$=$

$$

$$

$2$

$+$

$8$

$$

$+$

$7$

$,$ determine the s$-$domain output voltage for vin$($t$)$ equal to $($a$)3$u$($t$)$ V; $($b$)25$e$2$tu$($t$)$ V; $($c$)4$u$($t $+1)$ V; $($d$)2$ sin $5$t u$($t$)$ V$.$