The ss$-$domain transfer function, H$($s$)$H$($s$),$ can be used to relate the ss$-$domain input, X$($s$)$X$($s$),$ to the ss$-$domain output, Y$($s$)$Y$($s$),$ as described in the following equation.

Y$($s$)=$H$($s$)$X$($s$)$Y$($s$)=$H$($s$)$X$($s$)$

One important thing to note about this equation is that when X$($s$)=1$X$($s$)=1($corresponding to a unit impulse excitation$),$ Y$($s$)=$H$($s$)$Y$($s$)=$H$($s$),$ and likewise, y$($t$)=$h$($t$)$y$($t$)=$h$($t$).$ In this way, the transfer function can be used to investigate the natural response and the transient components of a circuit independent of the excitation function.

In the circuit above, the input function isvg$=2580$te$5$t$24$e$5$tvg$=2580$te$5$t$24$e$5$t$.$ WhenR$=100$R$=100,$ the output voltage can be described by the equationvo$=50$te$5$tvo$=50$te$5$t$.$