Vibrations in a Uniform Beam: A Physical Application of Differential Equations

• Main Author: Pfister, Jamie Nicole
• Format: Others
• Published: OpenSIUC 2013
• Online Access: https://opensiuc.lib.siu.edu/theses/1324; https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=2338&context=theses

To an untrained eye, a differential equation may appear to be just a conglomerate of mathematical symbols and operators. However, one of the most interesting aspects of differential equations is that an equation can be used to represent a physical situation. When a differential equation models a physical phenomenon, there is physical meaning behind the conditions placed on the equation and the solution has physical meaning as well. In this paper, we consider a differential equation that models transverse vibrations of a uniform beam. We begin with a brief discussion and explanation of the basics of differential equations and the important characteristics of them. Then we explore some of the theoretical background needed to solve the problem we are specifically interested in. After solving the boundary value problem, we will analyze and draw conclusions about what the solutions tell us is happening physically.