Comment by dmvaldman | Hacker News Reader

Comment by dmvaldman | Hacker News Reader

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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.

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 < 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)

thanks, that's much nicer indeed.

awesome! at 60 seconds my theory is confirmed! thanks

Don't miss the moiré patterns in the wires.

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

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.

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