A closed form solution of the run-time of a sliding bead along a freely hanging slinky

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

Abstract

The author has applied Lagrangian formalism to explore the kinematics of a bead sliding along a frictionless, freely hanging vertical Slinky. For instance, we derived a closed analytic equation for the run-time of the bead as a function of the traversed coil number. We have applied Mathematica to animate the 3-dimensional motion of the bead. The derived run-time is incorporated within the animation to clock the bead's actual motion. With the help of Mathematica we have solved the inverse run-time equation and have expressed the traversed coil number as a function of the run-time. The latter is applied to further the analysis of the problem conducive to analytic time-dependent equations for the bead's vertical position, its falling speed and its falling acceleration, and its angular velocity about the symmetry axis of the Slinky. It is also justified that a Slinky is a device capable of converting the gravitational potential energy of a sliding bead into pure rotational energy.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsMarian Bubak, Geert Dick van Albada, Peter M. A. Sloot, Jack J. Dongarra
PublisherSpringer Verlag
Pages319-326
Number of pages8
ISBN (Print)3540221298
DOIs
StatePublished - Jan 1 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3039
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Sarafian, H. (2004). A closed form solution of the run-time of a sliding bead along a freely hanging slinky. In M. Bubak, G. D. van Albada, P. M. A. Sloot, & J. J. Dongarra (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 319-326). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3039). Springer Verlag. https://doi.org/10.1007/978-3-540-25944-2_41