A ring of radius R carries a uniformly distributed charge `+Q`. A point charge `-q` is placed on the axis of the ring at distance 2R from the centre of the ring and released from rest. Will the particle execute simple harmonic motion along the axis of the ring ?

Explanation

Yes, but motion is simple harmonic only when charge `-q` is not very far from the centre of ring on its axis.
Otherwise far from the centre of ring on its axis.
Otherwise motion is periodic, but not simple harmonic in nature.