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

The resonant configurations and normal frequencies of a loaded hanging chain that is rotating uniformly about the vertical are examined for theoretical and experimental perspectives. The chain is assumed pinned at both ends, with an extra load added to the lower end for stability. The equation of motion for this system is solved and it is shown that the various resonant configurations of the chain are described by Bessel functions of order zero. The normal frequencies are obtained and the predictions of the model are compared to experiment. Time-exposure photographs are presented to illustrate the shape of the various normal modes.