Natural configurations and normal frequencies of a vertically suspended, spinning, loaded cable with both extremities pinned

Abstract

The resonant configurations and normal frequencies of a heavy elastic cable that is hanging in the field of gravity and is rotating uniformly about the vertical are examined from a theoretical perspective. The cable is assumed pinned at both extremities, with an extra load added to the lower one for stability. The equation of motion for this system is obtained and solved exactly. It is shown that the various resonant configurations of the cable are described by Bessel functions of order zero. The normal configurations and frequencies are obtained and the configuration of the cable in its lowest mode is presented as a photograph of demonstrations effected on three different samples. The results presented in this note would be useful for students in intermediate or advanced courses in classical mechanics, computation physics or waves and vibrations. © 2008 IOP Publishing Ltd.