WKB approximation for a mass moving on a taut string

Abstract In this paper, the motion of an inertial particle on a massless string under tension is analyzed. The study is conducted using the WKB approximation and asymptotic matching to describe the trajectory followed by the particle, as well as its fundamental parameters, such as the oscillations experienced by the mass, the maximum deformation of the string during the particle’s path, and the discontinuity between the particle’s position and the endpoint of the string. Finally, the obtained results are compared with numerical solutions to the problem, showing good agreement between both approaches.