What is the solution to the inverse Laplace transform of a given integral?

[TyErd]

Homework Statement

I've attached the multiple choice question

Homework Equations

The Attempt at a Solution

I inversed laplaced the problem and i get an answer of 3 H(t-3) sin(9(t-3)) which isn't any of the options so I chose F but that was wrong. So far I've confidentally eliminated B,C and now F. A D and E remain. I tried using the convolution integral that yields me a different answer as well so I am really confused here

 

[TyErd]

okay the answer is E. I already have 3 H(t-3) sin(9(t-3)). F(s) is H(t-3) and G(s) = sin(9(t-3)) but then when i write it as a convolution integral, shouldn't the t's be replaced with u instead of replacing the 3 as it is shown.

 

[TyErd]

it's cool i got it.