Wheaton College Norton, Massachusetts
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Physics faculty experiment with light, create art

pendulum1

These artistic images (above and below) document an experiment in physics conducted recently by Assistant Professor of Physics and Astronomy Dipankar Maitra, with the help of a few colleagues.

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Maitra removed one of the two chaotic pendulums that usually hang in the Physics Department hallway and attached an LED to the bottom, then mounted the device onto the edge of a sturdy bench in Professor of Physics John Collins’ laser spectroscopy lab. With additional guidance from Associate Professor of Physics Jason Goodman, they turned off all the lights in the lab except the LED and captured the pendulum’s movement in a series of 30-second long-exposure photographs.

The result is the brilliant image you see above.

So what is a “chaotic pendulum”? We asked Professor Maitra that exact question. Here’s what he had to say:

What is a chaotic pendulum?

A chaotic pendulum is really composed of two pendulums, with one pendulum attached to the end of the other. The ones we have are made plates of aluminum, pivoted on ball bearings so that they can swing quite freely. They were purchased a couple of years ago.

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A second chaotic pendulum hangs in the hallway in the Physics Department.

 

What do you mean when you say the pendulum’s behavior is “deterministic” and yet “chaotic”?

It is deterministic in the sense that its motion is completely determined by the laws of classical mechanics (i.e. it obeys Newton's laws of motion, laws of gravity, and conservation principles like conservation of mass, energy, conservation of linear and angular momentum, etc.). So in principle one could compute its motion if the starting conditions were fully known.

However, the motion of this type of pendulum is extremely sensitive to the starting conditions. A very minute, imperceptible difference in the starting conditions (e.g. a few air molecules hitting the pendulum one way or another when it was initially set to motion) eventually makes the pendulum move completely differently. Since in the real world we cannot tune the starting conditions to be that exactly same, therefore just like the "butterfly effect" in weather, there is no way to predict the motion of this pendulum, and hence we call the motion chaotic.

That said, I should add that the motion of this pendulum is not always chaotic. If you set it up in special ways, e.g. by giving it a very slight nudge so that the swings are rather small, then the motion can be predicted quite well. However for most cases, and especially the way we release it from the top, the motion is chaotic.