I also know from the problem that c=0 (no damping) and x(0) = 2m and x'(0) = 0.

ƩF = ma
ma = -cx' - kx, a = x''
mx'' + cx' + kx = 0 and since c=0
mx'' + kx = 0

Nothing out of the ordinary or unusual...but where the heck/how the heck do I include the unit impulse? From reading the textbook I have the impression that

mx'' + kx = ∂(t - 2∏)

and laplace [∂(t - 2∏)] = e^(-2∏s)

If my assumption is correct, I can do the problem.

Wolfram alpha (which instructor says is a legit method to solve this) says that my laplace is invalid, so I think somewhere I don't understand the unit impulse thing.