Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic
The problem is that you are analyzing sine and cosine without using a smooth window e.g a Hanning window. Your phase range is from -100 to 100 giving 100 / $\pi$ = 31.83 periods.This means that you have a discontinuity at the end of the FFT time record. So you are not analyzing a sine or cosine as you believe. Using a Hanning window will suppress the discontinuities and give a more meaningful result.