$10-42$ There is no initial energy stored in the circuit in Eigure P$10-41.($a$)$ Transform the circuit into the s domain and formulate node$-$voltage equations. $($b$)$ Show that the solution of these equations for V $2($s$)$ in symbolic form is V$2($s$)=($R$1+$R$2)$LCs$2+($R$1$R$2$C$+$L$)$s$+$R$1$R$1$V$1($s$)($c$)$ Identify the natural and forced poles of V$2($s$).($d$)$ Find v$2($t$)$ for v$1($t$)=2$u$($t$)$V$,$R$1=$R$2=1$k$,$L$=0\mathrm{.}1$H$,$ and C$=1$F$.$