We see a pendulum moves right and left or we also see the motion a spring expanding and contracting [Fig (a)]. We see that in both the cases the bodies repeat their motion. This type of motion is called periodic motion. So we can say, that if the motion of a body is such that at regular interval the motion of the body repeats, then that motion is called periodic motion.
If the motion of particle of a body is such that it crosses from the same direction a particular point in its path of motion at regular interval, then that motion is called periodic motion.
The oscillatory motion and the wave motion are examples of the periodic motion.
In periodic motion the moving path is fixed and at regular interval the body crosses a particular motion of the path from the same direction. This path of motion may have geometric shape. e.g., linear path, circular path, elliptical path etc. or not. If a body suspended from a spring is released after pulling it slightly downward, it will continue to move up and down periodically. It is observed that the body in its path of motion passes a particular from up to down or from down to up at regular interval. This motion of the body is a linear Periodic Motion. If a piece of stone fastened by a thread is rotated at constant angle velocity, it revolves in rational Periodic Motion.
The earth moves round the sun in elliptical orbit. At one year interval this rotation of earth repeats. This is the example of elliptical periodic motion.