The motion which repeats itself in equal intervals of time is known as periodic motion.
Because the motion of a swing also repeats after some intervals so, the motion of the child on a swing is periodic.
Simple harmonic motion is also a special case of periodic motion.
Examples of periodic motions are the motion of a pendulum, the vibration of a guitar string, the rotation of the Earth about its axis, the revolving of the Earth around the Sun, and the revolving of the Sun around the center of the Galaxy, etc.
Thus, the motion of a child on a swing is a periodic motion.