Free Vibration:
If the effect of forces other than the restoring force is negligible on a vibrating body, its motion is called a free vibration.
Forced Vibration:
If an external periodic force is applied to a freely vibrating body, the body tries to maintain its vibrations at its own frequency, but after some time, the body begins to vibrate with the frequency of the applied periodic force. Such vibration of a body is called a forced vibration.