At the park, Rashmi watches her little brother on a swing and says the swing is in periodic motion…

Why

Sparsh has noticed something true: the seat doesn't move in a straight line; it follows a curve, part of a circle centred on the bar. But circular motion means going round and round along a circle — like the tip of a fan blade or a cabin on a giant wheel — and a swing never goes all the way round. It moves forward along its curved path, stops, comes back, stops, and goes forward again, repeating the same to-and-fro movement in equal intervals of time. Motion that repeats itself after a fixed interval is periodic, and to-and-fro periodic motion like this is also called oscillatory motion, just like a pendulum's. Test: time how many seconds one full swing (forward and back) takes, then time the next few — each takes about the same time, and the seat never passes over the top of the bar. Rashmi is right: a swing's motion is periodic, to-and-fro motion, not circular motion.