Forced oscillations

An oscillator that is driven by an external periodic agency in order to overcome damping (rather than merely to compensate for the exact energy lost, as in maintained oscillation) is called a forced or driven oscillator. When the external periodic force is first applied, the body initially tends to vibrate at its own natural frequency, but this initial (transient) response dies away due to damping, and the body eventually settles down to vibrate steadily at the frequency of the applied external force -- not at its own natural frequency. Such steady-state vibrations, running at the driving frequency, are called forced vibrations. A concrete example is the sound board of a stringed instrument: the board itself has its own natural frequencies, but once the strings are bowed or pluck …