Laplace Transform simpilification

[gnittel]

Homework Statement

Is there a simplified Laplace transform of

The Attempt at a Solution

This is actually a three part question, I was only able to solve it when q is 0 or pi/2. but i can't seem to figure out the general solution.

 

[danago]

You could apply the cosine expansion identity to get:

$$re^{ - mt} \cos (pt + q) \equiv re^{ - mt} [\cos (pt)\cos (q) - \sin (pt)\sin (q)]$$

In which case it should now be easy to use a standard table of laplace transforms to get the answer you are looking for.

(I am assuming that r, m, p and q are all constants)