$($a$)$ Convert the circuit shown in Figure$-6$ to its Laplace equivalent.

$[10]$

$($b$)$ Solve the output voltage $\backslash (\backslash$mathrm$\{$v$\}(\backslash$mathrm$\{$t$\})\backslash )$ in the time domain, at $\backslash (\backslash$mathrm$\{$t$\}\backslash$geq $0\backslash ).$

$[10]$