L37 : Forced Vibration (damped, undamped)

Vibrations that take place under the excitation of external forces are called forced vibrations. When the excitation is oscillatory, the system is forced to vibrate at the excitation frequency. If the frequency of excitation coincides with one of the natural frequencies of the system, a condition of resonance is encountered, and dangerously large oscillations may result.

The French mathematician J. Fourier (1768-1830) showed that any periodic motions can be represented by a series of sines and cosines that are harmonically related. Therefore, the study of forced vibration under the action of a harmonic excitation force is of much relavance.