Question

find the Laplace transform of e^(-t/2)cos(2(t-pi/8)). I know that for e^(at)coskt you get (s-a)/((s-a)^2+k^2), but what happens as a result of the -pi/8 part?

Answer 1

Write down the Laplace transform integral explicitly and evaluate it. It's really not that bad.

Answer 2

alternatively, evaluate the Laplace transform of
\[ e^{zt + w} \]
where z and w are complex numbers. Then take the appropriate linear combination and values of z and w for your function.