I am doing this homework question on Mastery Physics and I do not understand why this field would make a particle have Simple Harmonic Motion behaviors. Here is the question:
Imagine a small metal ball of mass m and negative charge $−q_0$. The ball is released from rest at the point $(0,0,d)$ and constrained to move along the $z$ axis, with no damping. If $0 < d ≪a$, what will be the ball's subsequent trajectory?