Hyperbolic cosine function in physics

TL;DR: In this article, the hyperbolic cosine function is used to model the dynamics of a beaded chain falling from the edge of a table, when the distance between the two poles is varying.

Abstract: The catenary is the shape that an electric cable takes under its own weight if suspended only at its ends between two pylons. A rope hung between two masts is also described with a catenary equation which is based on the hyperbolic cosine function. We propose here to approach the hyperbolic cosine function with two simple experiments using a beaded chain. We first study the static form of the chain whose ends are suspended between two poles, when the distance between the two poles is varying. Then, we study the dynamics of the same chain falling from the edge of a table. The simplicity of these two experiments, which can be done at home, makes them appropriate for undergraduate students interested in practicals.