An Analysis Of Resonant Frequencies For A Hanging Chain Of Variable Masses

Abstract

The thesis problem finds its roots in wave mechanics. Ex- amine a hanging chain of vibrating rods, each of length r, as illustrated on the previous page. Although the individual lengths of the rods are the same the individual densities might not be. However, assume that the densities of all of the rods are evenly- distributed. Thia way the kinetic and potential energy terms will have the same general form, only the mass terms will vary in magnitude, f ran rod to rod. Given the above, the object is to determine the resonant frequencies of the system under certain assumptions.