Driven Nonlinear Oscillations of a String Available to Purchase

Nonlinear vibrations of a string may become unstable when the string is driven with sufficient amplitude near resonance. This paper describes the experimental conditions under which transverse oscillations of a horizontal string, driven in the vertical plane, become unstable. It is found that the planar oscillations become unstable in two different ways. One instability involves a spontaneous growth or decrease in the amplitude of the driven vertical motion. The other instability involves the spontaneous appearance of a transverse horizontal component of vibration perpendicular to the driving force, thus leading to a whirling or nonplanar motion of the string. The paper also describes the response of the nonplanar mode of oscillation, and it is found, for example, that for certain conditions the driven vertical component of oscillation decreases in amplitude when the driving level is increased. The experimental results agree qualitatively with theoretical predictions based in part on the work of Anand [J. Acoust. Soc. Amer. 46, 667–677 (1969)].