Transverse vibration of a moving string: A physical overview

This paper presents two physical explanations for the transverse oscillation of a moving string in terms of: (a) transverse waves propagating longitudinally, and (b) forces acting on a taut moving string due to oscillation. The first explanation leads to the closed-form solutions for the moving string directly from considerations of propagating transverse waves. The second explanation, based upon coupling of natural modes in time due to Coriolis actions, leads to a double-sine series solution of the equation of motion. The Galerkin method is shown to give matrices which are identical to those resulting from the coupled normal-mode solution.