$(20$ points$)$ The switch in Figure $4$ will be closed at $t=0s.$ Find the voltage across the capacitor, $v(t),$ for $t>0.$

Figure $4$: Circuit for Problem $4.$

$($a$)$ Find the initial voltage across the capacitor, $v(0).$

$($b$)$ Determine the initial current through the inductor $i(0)$; mark its direction in Figure $4.$

$($c$)$ Calculate the values of $$ and ${}_0.$

$($d$)$ Determine the damping status of $v(t).$

$($e$)$ Find the voltage $v(t)$ for $t>0.$

SOLVE ASAP