Authors: James A. Smith
This document attempted to obtain analytical solutions for the "Falling Slinky" in three ways. The first two, which used the wave equation, failed for different reasons. The first attempt used Fourier series, which could not satisfy the initial and boundary conditions. The second attempt used Laplace transforms; this method did give a solution, which correctly predicted the acceleration of the center of mass, but which predicted that the upper part of the Slinky should "fall through" the lower part, which is impossible. This false prediction is not a defect of the use of Laplace transforms, but an artifact of the use of the wave equation to treat the falling Slinky, which is a shock-wave phenomenon. The third attempt at a solution used the impulse-momentum theorem, obtaining a result whose predictions are internally consistent, as well as agreeing with empirical results. However, we must point out that the model used here treats only the Slinky's longitudinal behavior, ignoring its torsional behavior.
Comments: 25 Pages. Document is in Spanish
[v1] 2016-09-23 20:11:08
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