

15 uncoupled simple pendulums of increasing lengths dance together - SandB0x
http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80863&pageContentId=icb.pagecontent341734&state=maximize&view=view.do&viewParam_name=indepth.html#a_icb_pagecontent341734

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no_gravity
This made curious what patterns emerge when the objects move along circles
instead. So I made this 10 minute hack to simulate it:

<http://www.gibney.org/spiral_clock>

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kmm
Very pretty. It's a lot less crowdy if you change line 105 in your script to

    
    
      var speed =(nr_elements - i)/1000;

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no_gravity
Yeah, then the inner objects move faster and the outer objects move slower. I
find it hard to say, which version I prefer.

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Someone
Physics prefers that change, at least when gravity drives the motions.

If you adjust the periods as distance^1/3, you get a simple model for a solar
system.

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dmvaldman
it seems as if there is another interpretation lurking here... that you can
also explain this phenomenon as a single wave of increasing frequency in time
observed at 15 points. Because of the discrete nature of the points, there is
an aliasing effect as the wavelength of the wave gets shorter. For instance,
once the wavelength is equal to the spacing between pendulums, all pendulums
will line up. When the wavelength is twice that of the pendulums, they will
seem to alternate, etc.

This explains the awesome visual effect of this experiment. Though I'm not
exactly sure why adjusting the lengths of the pendulums would mimic a wave of
traveling with ever increasing frequency. Maybe it has something to do with
dispersion (we see an overlap of waves that travel at speeds proportional to
their frequency/length)?

A great experiment would be to have two of these pendulum systems side by
side, except one is made of 30 pendulums at half the spacing. Then when the 15
pendulum system is lined up, the 30 system should be alternating,etc.

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gautier
You wish for it, HTML5 delivers. <http://pepsdev.com/pendulums/>

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city41
A slight tweak to draw the pendulums too makes the simulation look much nicer:

    
    
          function draw (Ls, t, h) {
             // only for in the program, needed?
            for (var i = 0; i < Ls.length; i++) {
              ...
              ctx.lineTo(h * L, 0)
              ctx.arc(h * L, 0, 6, 0, 360)
              ctx.stroke()
              ctx.fill()
              ...
            }
          }
    

to do it right you really need to start another path, but this works fine in
Chrome (looks little wonky in Firefox)

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gautier
thanks, that's much nicer indeed.

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kmm
Related: <http://wheelof.com/whitney/index.php?var=v6> Warning: Flash + sound

The mathematics behind this are pretty simple. It's just that the human mind
is great at picking up patterns.

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Groxx
That is an awesome site. Thanks! I've never seen anything like that before.

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5hoom
Hypnotic video.

Only vaguely related, but this reminds me of a story a couple of years back
involving a machine learning system that was able to derive the laws of
Newtonian physics from observing the motion of a hinged pendulum.

[http://worldsciencefestival.com/videos/robot_learning_rebuil...](http://worldsciencefestival.com/videos/robot_learning_rebuilding_newton)

There's a lot of information buried in the motion of these objects :)

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impendia
The Exploratorium in SF has one of these you can play with. Show up at their
monthly "After Dark" and you won't have to compete with the kiddos.

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rasur
You can see a physical example of this at Technorama (in Switzerland) for
those of you with kids that enjoy a good day out.

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voidmain
Here's my attempt (requires WebGL, realistically only works in Chrome):

[http://www.glowscript.org/#/user/David/folder/Public/program...](http://www.glowscript.org/#/user/David/folder/Public/program/DancingPendulums)

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nilaykumar
Here's an exposition on the math:
[http://hippomath.blogspot.com/2011/06/pendulum-waves-
mathema...](http://hippomath.blogspot.com/2011/06/pendulum-waves-mathematical-
description.html)

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Roritharr
I've seen this setup in the Mathematicum which is a museum dedicated to math,
in Gießen, Germany.

I really didn't know this was a phenomenon..

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sixtofour
It looks like a sorting algorithm visualization.

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matej_kosik
s/vinostroj/vlnostroj

