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.

A to and fro motion about a mean position having a definite period is a periodic motion.

Let us analyse each condition-

(a) Here, the motion of the swimmer between the banks of the river is to and fro. But it cannot be said to have a definite period as we do not know how much time the swimmer will need to complete each trip. Hence, it does not represent a periodic motion.

(b) When a freely suspended magnet is displaced from N-S direction and released, it oscillates periodically about the mean position. Hence, it is a periodic motion.

(c) The hydrogen molecule rotates about its centre of mass which constitutes a periodic motion.

(d) When an arrow is released from a bow, it just goes in one direction and doesn’t make oscillations back and forth. Hence, the motion is non-periodic.