When an input voltage of $30$u$($t$)$V$30$u$($t$)$V is applied to a circuit, the response is known to be

vo$=(50$e$8000$t$20$e$5000$t$)$u$($t$)$Vvo$=(50$e$8000$t$20$e$5000$t$)$u$($t$)$V$.$

What will the steady$-$state response be if vg$=120$cos$6000$tVvg$=120$cos$6000$tV$?$