Green's Functions, Wave Equation

[Master J]

In solving the driven oscillator without damping, I need to solve the integral

{ exp[-iw(t-t')] / (w)^2 - (w_0)^2 } .dw

where w_0 is the natural frequency.

I know the poles lie in the lower half plane, yet I cannot see why. If (t - t') < 0, the integral is zero. I am not exactly sure how this?

 

[dextercioby]

Aren't the poles situated on the real axis at $\pm \omega_0$ ?

 

[Master J]

Isn't it the idea though, that to integrate it, you let w be complex, so that when the real part equals zero, there is still the imaginary part?