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15 uncoupled simple pendulums of increasing lengths dance together

sciencedemonstrations.fas.harvard.edu

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Re: 15 uncoupled simple pendulums of increasing lengths dance together

#11

Post by Retric »

dmvaldman wrote: post #5

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…

The hard part about understanding this is modeling the position of each pendulum easily. If you want something that cycles from 0 to 1 and back try: Absolute value of (x mod 2 + 1) note:drop the abs to see direction. If they all cycle in 60 seconds it's easy to see that any cycle will start over. At 1/2 the full cycle time they will split into left and right sides etc. Now, work backward after the fastest ball does 4 cycles you can see something that looks nothing like a sine wave.

However, you now need to substitute that position as time into the pendulum equation. At which point you see the sine wave behavior of sticking near the edges as the ball picks up momentum followed by a fast transverse through the center. Still, it's not really a sine wave but it's fairly close. To get a true sine wave all the pendulums would need to be the same length and the balls dropped the same distance but at slightly different times. However, in the experiment they are close to the same length and distance fallen so it looks about right.

Re: 15 uncoupled simple pendulums of increasing lengths dance together

#12

Post by gautier »

dmvaldman wrote: post #5

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…

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

Re: 15 uncoupled simple pendulums of increasing lengths dance together

#13

Post by city41 »

gautier wrote: post #12
dmvaldman wrote: post #5

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…

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

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

Re: 15 uncoupled simple pendulums of increasing lengths dance together

#14

Post by gautier »

city41 wrote: post #13
gautier wrote: post #12

Earlier quoted context omitted.

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

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

thanks, that's much nicer indeed.

Re: 15 uncoupled simple pendulums of increasing lengths dance together

#18

Post by dmvaldman »

gautier wrote: post #12
dmvaldman wrote: post #5

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…

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

awesome! at 60 seconds my theory is confirmed! thanks

Re: 15 uncoupled simple pendulums of increasing lengths dance together

#19

Post by Someone »

no_gravity wrote: post #8
kmm wrote: post #7

Earlier quoted context omitted.

Very pretty. It's a lot less crowdy if you change line 105 in your script to var speed =(nr_elements - i)/1000;

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

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.

Re: 15 uncoupled simple pendulums of increasing lengths dance together

#20

Post by billybob »

dmvaldman wrote: post #5

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…

My friend's version: http://sorryrobot.com/pendula/
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