Which of the following examples represent periodic motion?
$(a)$ $A$ swimmer completing one (return) trip from one bank of a river to the other and back.
$(b)$ $A$ freely suspended bar magnet displaced from its $N-S$ direction and released.
$(c)$ $A$ hydrogen molecule rotating about its centre of mass.
$(d)$ An arrow released from a bow.

(B, C) and $(c)$
The swimmer's motion is not periodic. The motion of the swimmer between the banks of a river is back and forth. However,it does not have a definite period. This is because the time taken by the swimmer during his back and forth journey may not be the same.
The motion of a freely-suspended magnet,if displaced from its $N-S$ direction and released,is periodic. This is because the magnet oscillates about its position with a definite period of time.
When a hydrogen molecule rotates about its centre of mass,it comes to the same position again and again after an equal interval of time. Such motion is periodic.
An arrow released from a bow moves only in the forward direction. It does not come backward. Hence,this motion is not periodic.