# Phase difference betwen 2 signals, 1 signal with unknown function

I understand this question may have been addressed however I have a major difference.

I started out with a sinusoid of form A*sin(2 pi freq t + phase) and I know all the components, this represents a force a system and produces a response that has a delay and that is periodic in a way, no fully sinusoidal though (I can post pics and any relevant material).

Thus for the response signal I know the frequency and the time vector, I need to find the amplitude and the phase. I have been using FFT but I am not sure if that is the best way. Can someone please help me out here, this seems fairly simple, however I am struggling, Thank you