Effective solution of the problem of motion of an infinite string with an attached point mass

Abstract

The Cauchy problem for the equation of motion of a string with a point mass is considered. By applying the convolution method for Fourier expansions, the solution of the problem is expressed in the form of quadrature rules in terms of the solution of the classical Cauchy problem with no point mass with the same equation and initial functions. As an example, a finite-form solution of the problem is found and the corresponding plots of the string near the point mass are constructed with a constant time step.