Imagine a string of a fixed length allowed to hang under the influence of gravity, and with the two endpoints suspended at fixed points of distance less than or equal to the length of the string. The string forms some U-shaped curve, called a catenary. It turns out that this curve matches to the graph of a hyperbolic cosine function $\cosh(x) = \frac{e^x + e^{-x}}{2}$.

Below is a physical simulation of this scenario, where the curve is modeled as a finite number of point masses connected by friction-ful springs. Because the string can stretch in this simulation (as opposed to fully taut as in the prompt scenario), the equilibrium position will be slightly incorrect, but we can ameliorate this by sending the spring constant to $\infty$.