Free oscillations

If an oscillator is displaced and then released it will begin to vibrate. If no more external forces are applied to the system it is a free oscillator. Example – When you push a swing once and leave it, it will come to a halt after sometime. The oscillations are said to be damped oscillations as it fades out and stops after sometime.

Forced oscillations

If a force is continually or repeatedly applied to keep the oscillation going, it is a forced oscillator.

Going by the same swing example, if the swing is pushed each time it reaches a certain point it behaves as a forced oscillator and will continue to swing for as long as energy is supplied.

Resonance

If the driving force, applied to the oscillating system, as exactly the same frequency as its natural frequency, the amplitude of the oscillation, increases to the maximum value. The body is said to be in Resonance. The amplitude will be maxim

The natural frequency that the swing wants to oscillate at is called its resonant frequency. If the pusher pushes at the swing s resonant frequency, the amplitude of oscillation will build up. With each period, the pusher will add more energy to the system. Eventually, what usually happens is that energy supply equals energy loss (to damping), and the amplitude stabilises at some large value