Mathematical analysis of a freely falling slinky

Abstract

If you release a slinky hung in midair from its initial stationary position, you can observe something interesting: the bottom of the slinky is at rest in midair for a while. Among physicists, this phenomenon is well known and has been discussed from the physical point of view. In this paper we deal with the problem of a freely falling slinky from the purely mathematical point of view. Through the rigorous mathematical process we obtained an explicit formula which describes the motion of the freely falling slinky and it turns out that this is a solution to an inhomogeneous wave equation. Our work gives the mathematical justification of the results obtained by physicists.