An oscillator that is set into motion and left alone will oscillate at its own frequency. This is the oscillator’s natural frequency.
When the oscillator is being forced to oscillate at a different frequency by an external driving force, then it is said to be executing forced oscillations.
The frequency the oscillator is forced to vibrate at is known as the driving frequency.

Damped vibrations

Unless an oscillator is maintained by some source of energy, its amplitude of vibration will become progressively smaller - the motion is said to be damped. The decrease in amplitude occurs because some of the energy of the oscillating system is used to overcome resistive forces. The greater the resistive forces, the greater the damping, i.e the amplitude of vibration will be reduced much quicker.

With light damping gradually reduces in amplitude but takes a long time to disappear.

With heavy damping the oscillator might not even complete one cycle or if does return to its equilibrium position, it will take a very long time.

Critically damped
With critical damping the oscillator returns as quickly as possible to the equilibrium without overshooting (going past the equilibrium position).

When the driving frequency is the equal to the natural frequency of the system that is being driven, it oscillates with maximum frequency. This is called resonance.

Effect of resonance on wine glass

Millenium Bridge

Tacoma Narrows bridge