When a particle undergoes simple harmonic motion, its acceleration...

For a particle executing simple harmonic motion, the restoring force acting on it is directly proportional to its displacement from the mean position and is directed towards the mean position.

$F = -kx$

$ma = -kx$

$a = -\dfrac{k}{m}x = -\omega^2 x$

Thus, the acceleration of the particle is directly proportional to its displacement from the mean position.