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

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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) 319-326 8 Lecture Notes in Computer Science 3039 Published - 2004

### Fingerprint

Angular velocity
Potential energy
Animation
Closed-form Solution
Clocks
Kinematics
Mathematica
Coil
Gravitational potential energy
Vertical
Motion
Symmetry
Closed
Energy

### All Science Journal Classification (ASJC) codes

• Theoretical Computer Science
• Computer Science(all)

### Cite this

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title = "A closed form solution of the run-time of a sliding bead along a freely hanging slinky",
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.",
author = "Haiduke Sarafian",
year = "2004",
language = "English (US)",
volume = "3039",
pages = "319--326",
journal = "Lecture Notes in Computer Science",
issn = "0302-9743",
publisher = "Springer Verlag",

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In: Lecture Notes in Computer Science, Vol. 3039, 2004, p. 319-326.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A closed form solution of the run-time of a sliding bead along a freely hanging slinky

AU - Sarafian, Haiduke

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

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