Initial boundary value problems associated with a spinning string

Abstract

A model is developed for the transverse vibrations of a spinning string. This model involves a pair of coupled second order partial differential equations for the components of the transverse displacement along the string. Analytic solutions are presented for various choices of initial and boundary conditions, in the case of semi-infinite strings and finite length strings (with fixed or variable length). Techniques used involve an extension of the standard d'Alembert solution of the one-dimensional wave equation and Fourier analysis. Graphical illustrations are presented.