Answer
$4\cos 3t+\frac{5}{3}\sin 3t$
Work Step by Step
Given: $F(s)=\frac{4s+5}{s^2+9}$
Using the Convolution Theorem
$L^{-1}[F(s)]=L^{-1}[\frac{4s+5}{s^2+9}]\\
=L^{-1}[\frac{4s}{s^2+9}]+L^{-1}[\frac{5}{s^2+9}]\\
=4L^{-1}[\frac{s}{s^2+9}]+5L^{-1}[\frac{1}{s^2+9}]\\
=4\cos 3t+\frac{5}{3}\sin 3t$
