Motions of a Stretched String Carrying a Moving Mass Particle

Abstract

A considerable amount of analytical work has been carried out in order to determine the effects of “traveling” loads on structures. Several methods—all approximate—have been used to predict the motion of a beam, along which a mass particle is constrained to move. An “exact” solution is presented here for a similar system in which a stretched string serves as support for the moving mass. Comparison with this system lends some insight into the more complicated beam problem. A singular behavior of the solution to the string problem suggests the possibility of an analogous singular behavior in the solution to the beam problem.