An explicit solution for the dynamics of a taut string of finite length carrying a traveling mass: the subsonic case

The authors investigate the linear vibrations induced in an elastic string by a loading point-like mass constrained to moving on it with constant horizontal velocity. Exact solutions are shown in the case of subsonic regime. The displacement is explicitly provided in terms of a power series determined by iteration, which is shown to converge to the solution of the problem. The presence of a discontinuity in the right extremum of the considered space interval is also shown both analytically and numerically.