Define : Natural oscillations, free oscillation and forced oscillation.

Explanation

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