Question

A voltage v(t)=2t^(2)e^(-3t) is passed through a delay line having a delay of 4 sec.Detrmine Laplace transform of the output voltage.

Answer 1

The LT of v(t) found using a table entry is

\[4/(s+3)^3\]
Multiply that by \[e ^{-4t}\] for the time delay to get
\[4e ^{-4t}/(s+3)^{3}\]

Answer 2

The table entry was
\[f(t)=t ^{n}e ^{at}\leftarrow \rightarrow F(s)=n!/(s-a)^{n+1}\]