Driving force in simple harmonic oscillator with exponential

[nacreousnereid]

Homework Statement

A particle in SHM is subject to a driving force F(t)= ma*e^(-jt). Initial position and speed equal 0. Find x(t).

Homework Equations

F = -kxdx = mvdv
F(t) = F(0)*e^(iωt)
x(t) = Acos (ωt +φ)

The Attempt at a Solution

I have no idea how to deal with the exponential term. I know I can put the t in e^(-jt) in terms of v, but that makes integration awfully messy. Any tips? Thanks!

 

[nasu]

There are two forces here: the elastic force and the driving force. When you write Newton's second law you need to include both.
-Kx+F(t)=ma

This will result in a non-homogeneous second order differential equation.
A possible solution will be an oscillation with the same frequency as the driving force's frequency.