W. G. Unruh's succinct paper on the matter here.
When a Slinky is dropped, the bottom of the Slinky remains motionless as the top collapses towards it, making it appear to the observer as though the Slinky is levitating. By considering the Slinky as a tightly wound, pretensioned spring, the static equilibrium of a hanging Slinky was solved for using Hooke's law (Equation 1). This result was used to measure the spring constant of an actual metal Slinky. The motion of the Slinky after it is released at time t=0 was then solved for to derive an expression for the time over which the bottom of the Slinky remains motionless and the Slinky appears to levitate (Equation 7). This expression gave a value of t = 0.29 ± 0.05 seconds for the Slinky used in the experiments, which matches up very well with the experimentally measured value of t = 0.4 ± 0.1 seconds
It has been a few years away from this type of stuff (in a totally different area using math). The most important thing one can remember when going through grad school, "You CAN'T divide by ZERO!"