| Popis: |
The forced vibrations of stretched strings near their resonance frequencies exhibit several features that cannot be explained on the basis of the classical theory. As the driving frequency approaches resonance frequency, the increase in the amplitude of vibration of the string causes a change in its tension and the restoring force becomes nonlinear. Experiment shows that the amplitude response exhibits a downward jump while the driving frequency is being increased and an upward jump at a different frequency while the frequency is being decreased. Moreover, when the amplitude of vibration in the plane of the driving force reaches a certain critical value, which depends upon the magnitude of the driving force, the string acquires a component of motion in a direction normal to the plane of the string and the force. These phenomena are always observed in a more or less conspicuous manner, depending upon the magnitude of the force. When the restriction to infinitesimally small amplitudes of vibration (which is untenable near resonance) is removed, the motion of the string is governed by a pair of nonlinear, partial differential equations. Appropriate solutions of these equations show that the jump phenomena and the nonplanar vibration are the normal pattern of resonance behavior of stretched strings, however small the driving force may be. Response patterns and other results deduced from theory agree closely with those obtained from experiment. |
