Abstract
This paper discusses the oscillations of a spring (slinky) under its own weight. A discrete model, describing the slinky by N springs and N masses, is introduced and compared to a continuous treatment. One interesting result is that the upper part of the slinky performs a triangular oscillation whereas the bottom part performs an almost harmonic oscillation if the slinky starts with ‘natural’ initial conditions, where the spring is just pushed further up from its rest position under gravity and then released. It is also shown that the period of the oscillation is simply given by , where L is the length of the slinky under its own weight and g the acceleration of gravity, independent of the other properties of the spring.
Highlights
A slinky, invented in the 1940 by Richard James, is in the context of this paper a spring that is oscillates under its own weight without any additional mass attached to it with a quality factor high enough to observe the oscillations
Equations of motion are derived and solved for the discrete case where the slinky is described by N masses and springs
If the slinky is for instance pulled at n ≈ 0.4, the oscillations look very different
Summary
A slinky, invented in the 1940 by Richard James, is in the context of this paper a spring that is oscillates under its own weight without any additional mass attached to it with a quality factor high enough to observe the oscillations. There are many articles on a falling slinky [1, 2, 3] and the suspended slinky [4, 5]. This article studies interesting aspects of a suspended slinky. Equations of motion are derived and solved for the discrete case where the slinky is described by N masses and springs (section 2).
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