Differential Bessel Equations and the Oscillating Chain

Abstract

The modeling of many everyday problems is done through differential equations (DE). The oscillating current problem is no different from this and, since it is a problem that is easy to display and relatively understandable, we will discuss it in this article, with the aim of determining and interpreting its solution. We will not discuss in detail nor present the theory that deals with Bessel's equations and functions, however, we will present the theory that involves transforming a singular Bessel equation (not shown in its standard form) into its standard form, which exhibit the general solution as a linear combination of first and second species Bessel functions. Finally, having the solution of the Bessel equation that models the problem of the oscillating heavy current, we will find that the periodic movement depends exclusively on its length and the sequence of oscillation times shows the tendency of the movement to a stationary regime.