# Constrained Oscillations

## Constrained Oscillations

oscillations arising in any system under the influence of a variable external force (for example, the oscillations of a telephone membrane caused by an alternating magnetic field or the oscillations of a mechanical structure under a variable load).

The nature of constrained oscillations is determined by both the character of the external force and the properties of the system itself. When a periodic external force begins to act, the nature of the constrained oscillations changes with time (in particular, the oscillations are not periodic), and only with the passage of time do the constrained oscillations in the system become periodic, with a period equal to that of the external force (stable constrained oscillations). The greater the damping of the oscillations in a system, the faster the establishment of constrained oscillations in that system.

In particular, free (or inherent) and constrained oscillations arise simultaneously in linear oscillation systems when an external force is introduced; the amplitudes of these oscillations at the initial moment are equal, but their phases are opposite. After gradual damping of the free oscillations, only the stable constrained oscillations remain in the system.

The amplitude of the constrained oscillations is determined by the amplitude of the acting force and the damping in the system. If the damping is small, the amplitude of the con-strained oscillations depends essentially upon the correlation between the frequency of the acting force and the frequency of the system’s natural oscillations. As the frequency of the external force approaches the natural frequency of the system, the amplitude of the constrained oscillations grows sharply—resonance appears. In nonlinear systems it is not always possible to distinguish free and constrained oscillations.

### REFERENCE

Khaikin, S. E. Fizicheskie osnovy mekhaniki. Moscow, 1963.
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