The Falling Slinky

Consider a slinky that is held at one end while the rest of it is allowed to hang freely. If the slinky is released, then as it falls due to gravity it also shrinks in extent due to the contracting force in the slinky itself. A few years ago it was discovered that the net effect of these two changes exactly counteract each other at the bottom extent of the slinky and therefore the bottom of the slinky remains utterly motionless until the full slinky is complete compressed at which point the bottom edge begins to loose height as the whole thing falls together. In this paper, we describe a simple model that closely approximates the dynamics of a real slinky and we give a careful mathematical explanation for this phenomenon.