Forced Harmonic Oscillator
The oscillations of any real, damped oscillator can be sustained by applying an external force which supplies the necessary energy for the oscillations and compensates for the frictional losses. Of particular importance is an external harmonic force of the type
F = F0 cos ω t
Under the influence of such a force, it is observed that the object initially begins to oscillate with its natural frequency 
, but soon the free oscillations of the object die out, and finally the object performs harmonic motion of constant amplitude with frequency ω of the external force. Such a system is therefore called a driven or forced harmonic oscillator.
Thus, a forced harmonic oscillator eventually performs steady state oscillations of constant amplitude and frequency. The period, from the moment external force F starts to act till the time the system achieves the steady state, is called transient period. During the transient period, the free oscillations die out and steady motion is established. The transient period is equal to time constant 
, where 
is damping constant.
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