Vibration of Strings with Time-Varying Length : The Case Having a Weight at One End

Abstract

In this paper, free vibrations of a string with time-varying length and a weight at one end are analyzed. An equation of motion cannot be solved by the method of separation of variables because the length of the string varies with time. New variables of position and time are introduced which allow the equation of motion to be solved by Laplace transformation. Almost exact solutions of free vibrations induced by a distributed initial displacement are also obtained.