### 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 language | English (US) |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Marian Bubak, Geert Dick van Albada, Peter M. A. Sloot, Jack J. Dongarra |

Publisher | Springer Verlag |

Pages | 319-326 |

Number of pages | 8 |

ISBN (Print) | 3540221298 |

DOIs | |

State | Published - Jan 1 2004 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 3039 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'A closed form solution of the run-time of a sliding bead along a freely hanging slinky'. Together they form a unique fingerprint.

## Cite this

*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