# Generate random vibration with zero mean for the motion of a point in 3D space

I want to simulate a point that moves with random vibration around a mean position (let's say around the position $$[X, Y, Z] = [0,0,0]$$). The first solution that I found is to sum a couple of sinusoids for each axis, $$\sum_{i = 1}^n A_i \sin(\omega_i t+\phi)$$ where $$A_i$$ is a normal random amplitude, and $$\omega_i$$ is a normal random frequency. I have not tested the phase yet, so I leave it to zero for now. I generated figures of the expect normal distribution and equation results with the following approach. I tried multiple values of N and I'm not sure that the equation is giving a normally distributed results. Is my approach correct? Is there a better way to generate random vibration?