Slinky

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpaceCurves/Slinky.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Slinky.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Inititalization

Code

Slinky[{a_,w_,h_},t_]:={
Cos[t](1+a Cos[w t]),
Sin[t](1+a Cos[w t]),
h t+a Sin[w t]
}

Plot

g=ParametricPlot3D[Evaluate[Append[Slinky[{.4,40,.3},t],Red]],{t,0,5π},PlotPoints->1000,Axes->False]

LiveGraphics3D

<<Utilities`LiveGraphics3D`

WriteLiveForm["slinky.m",g]

Properties

Arc Length

ArcLength[Slinky[{a,ω,h},t],t,Assumptions->a>0&&ω>0&&h>0]

ArcLength[Slinky[{a,ω,h},t],t,Assumptions->a>0&&ω>0&&h>0]

Curvature

FullSimplify[Curvature[Slinky[{a,ω,h},t],t],a>0&&ω>0&&h>0&&t>0]

Torsion

FullSimplify[Torsion[Slinky[{a,ω,h},t],t],a>0&&ω>0&&h>0]