You have a simple harmonic oscillator. Where is its acceleration zero?

at mean position

Explanation:

In case of simple harmonic motion, there are two positions of the body which is oscillating.

One is called mean position and the other is extreme position.

there are two extreme positions and the mean position is in between these two extreme positions.

At mean position the velocity is maximum and the acceleration is zero but at the extreme positions, the velocity is zero but the acceleration is maximum.