Define: Natural oscillations,free oscillations,and forced oscillations.

(N/A) Natural Oscillation: When an oscillator is slightly disturbed from its equilibrium position and released,it starts oscillating. The oscillations performed by it in the absence of any type of resistive force are known as natural oscillations.
The angular frequency of natural oscillation is $\omega_{0}$ and the frequency is $f_{0}$.
Free Oscillation: When a system is displaced from its equilibrium position and released,it oscillates with its natural frequency. These oscillations are known as free oscillations.
The angular frequency of free oscillation is $\omega$.
Forced (driven) Oscillations: The oscillations executed by a system under the influence of an external periodic force are called forced oscillations.
The angular frequency of forced oscillation is called $\omega_{d}$,which is the angular frequency of the external force.
In practice,oscillations always occur in some medium; hence,some type of damping force is always acting on the system,and eventually,the oscillations die out with time. To sustain the oscillations,an external periodic force is required.
Example: When a child on a garden swing periodically presses their feet against the ground.