Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion.

Periodic motion, in physics, motion repeated in equal intervals of time. ... Periodic motion is performed, for example, by a rocking chair, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave.

Periodic Motion

Periodic motion refers to the motion that repeats itself after a regular interval of time. It is characterized by the motion of an object or a system that returns to its initial position and velocity after a certain period of time. The motion of a swing can be categorized as periodic motion because it exhibits the following characteristics:

1. Oscillation:
- A swing moves back and forth around a fixed point, which is usually a pivot point at the top.
- The swing oscillates between two extreme positions - the highest point and the lowest point.
- This back and forth motion is also known as swinging or pendular motion.

2. Regular Time Interval:
- The swing takes a fixed amount of time to complete one full swing, from the highest point to the lowest point and back to the highest point again.
- This time interval is constant as long as the swing continues to swing with the same amplitude and under the same conditions.
- The time period of the swing can be measured using a stopwatch or by counting the number of swings in a certain time frame.

3. Repeating Motion:
- The swing repeats its motion over and over again, following the same path and covering the same distance during each swing.
- This repetitive motion is the defining characteristic of periodic motion.

4. Amplitude:
- The amplitude of the swing refers to the maximum displacement or distance the swing moves away from the equilibrium position.
- When someone pushes a swing, it swings to a certain height on one side, then comes back to the equilibrium position, and swings to the same height on the other side.
- The swing's amplitude is determined by the initial push or force applied to it.

5. Periodic Force:
- The swing's motion is sustained by the force applied to it, typically by a person pushing it or by the force of gravity.
- The force acts periodically, as it is applied at regular intervals to maintain the swing's motion.

In conclusion, the motion of a swing is an example of periodic motion because it exhibits oscillatory motion, follows a regular time interval, repeats its motion, has an amplitude, and is sustained by a periodic force. Therefore, the correct answer is option 'C' - Periodic motion.