Undamped free vibrations: When a bob of a simple pendulum (in vacuum) is displaced from its mean position and left, it executes simple harmonic motions. The pendulum will continue to oscillate with the same time period and amplitude for any length of time. In such cases there is no loss of energy by friction or otherwise. In all similar cases, the vibrations will be undamped free vibrations.
Damped free vibrations: In actual practice, when the pendulum vibrates in air medium, there are frictional forces and consequently energy disappear in each vibration. The amplitude of swing decreases continuously with time and finally the oscillations die out. Such vibrations are called damped free vibrations.
Forced vibrations: The time period of a body executing simple harmonic motion depends on the dimensions of the body and its elastic properties. The vibrations of a body die out with time due to loss of energy. If some external periodic force is constantly applied on the body, it continues to oscillate under the influence of such external forces. Such vibrations of the body are called forced vibrations.