Forced oscillations and resonance

Forced oscillations:

• When the system oscillates without a periodic force being applied to it,its frequency is referred to as its natural frequency.
• Periodic force is force applied at regular intervals. 
• When a periodic force is applied to an oscillating system, the response depends on the frequency of the periodic force. The system undergoes forced oscillations when a periodic force is applied to it.
• example:

Resonance:

• Applied frequency = natural frequency of system  
• the amplitude of oscillations becomes very large. the lighter the damping in the system, the larger the amplitude becomes. the system is in resonance when the applied frequency equals the natural frequency,
• the phase difference between the displacement and the periodic force is 1/2π at resonance. the periodic force is then exactly in phase with the velocity of the oscillating object. 
• Applied frequency > natural frequency of system
• the amplitude of oscillations decreases more and more,
• the phase difference between the displacement and the periodic force increases from 1/2π until the displacement is π radians out of phase with the periodic force.

 = Resonance curves