Falling Non-Harmonic Slinkys

Schuenck P

Published on: 2022-08-27

Abstract

Slinkys that start from a stretched equilibrium position supported at the top and then released to fall under the influence of gravity exhibit the interesting behavior that the bottom of the slinky does not move until the collapsing top of the Slinky reaches the bottom. In this paper, we examine this problem using numerical methods to investigate whether this property holds for generalizations of the slinky physics such as changing the restoring force from the traditional Hooke’s law or considering random and non-uniform distributions of masses. For restoring forces, F, of the type F = k^p, where x represents the spring displacement and k the generalized spring constant, it is found that when p > 0, the bottom-doesn’t-move property holds, but when p < 0, the model shows complicated collapse patterns that in some cases depend on whether the number of modeled masses is even or odd.