$($a$)$ Laplace ty anstorm $C\{\frac{e^{3x}}{2}\}$

$(4$ marks$)$

$($b$)$ Inerse Laplace trof sorm $L^{-1}\{\frac{1}{2}\frac{4}{s-6}\}.$

$(4$ marks$)$

$($c$)$ For the spring$-$mass$-$damper systery of which input is the pring displacement $x_i($t$)(12$ marks$)$ and outy ut is the mass displacement $x_o(t),$ as shom in Figure Q$3($c$).$ Find transfer fimetion of the system, i$.$e$.\frac{x_0(s)}{x_i(s)}.$

$1$