$($a$)$ Find the transfer function Vo$($s$)/$Vi$($s$)$ of the circuit in Fig. $2$ with R $=(8)$ kW and C $=(6)$F$.$

$($b$)$ Find the zero$-$state output vo$($t$)$ if vi$($t$)=$ e$^(-4$t$)$ V$.$

$($c$)$ Calculate the natural frequencies of the circuit. Is the circuit stable?

$($d$)$ Calculate the steady$-$state output vo$($t$)$ if $($a$)$ vi$($t$)=2$ V and $($b$)$ vi$($t$)=$ sin$(1000$t$)$u$($t$)$ V$?$ Will an initial voltage of $1$V on each of the capacitors affect the solution? Figure $2$