Free, forced and resonant oscillations

Free oscillations: when a body capable of oscillation is displaced from its equilibrium position and then left free, it begins to oscillate with a definite amplitude and frequency. If the body is not resisted by any kind of friction, the motion continues. Such oscillation is called the free oscillation. The frequency of vibration depends on the intrinsic properties (shape, elasticity etc) of the body which is called as the natural frequency. The force acting on the on the system is the restoring force. For example, when a simple pendulum is displaced from its mean position and then left free, it executes free oscillations. The natural frequency of the simple pendulum is f= (¹/₂π) {root (l/g)}. In absence of frictional forces, the amplitude of the free oscillations would remain constant. However, in actual practice, a complete free oscillation cannot be obtained in nature.

Forced oscillations: when a body is maintained in a state of oscillation by an external periodic force of frequency other than the natural frequency of the body, the oscillation is called the forced oscillation. In such oscillation is equal to the frequency of the periodic force. The external applied force on the body is called the driver and the body set into the oscillations is called driven oscillator.

    Resonant oscillations: when a body is maintained in state of oscillations by a periodic force having the same frequency as the natural frequency of the body, the oscillations are called resonant oscillations. The phenomenon of producing resonant oscillations is called resonance. Note that the resonance is a particular case of forced oscillations in which the two frequencies are equal.