What is Periodic motion?
The motion which repeats itself in particular intervals of time is called Periodic motion. For example, a rocking chair.
Rocking chair
An object can perform a circular motion as well as a periodic motion at the same time. For example, a car moving along the circumference of a circle in equal intervals of time.
Car moving in circles
 What is Oscillatory motion?
A freely hanging object undergoing to and fro motion is called Oscillatory motion.
One oscillation is completed when the object moves from the mean position to the upper extreme, then to the other extreme and back to the mean position. For example, swinging of a swing, or a free pendulum.
Oscillating pendulum
 Is oscillatory motion periodic?
Every oscillation takes equal intervals of time to complete. Therefore an oscillatory motion is also periodic in nature. Hence, an oscillating pendulum undergoes oscillatory as well as periodic motion.