# Simple, Beautiful Physics: Video

May 4, 2011 15 Comments

This is one of the simplest but most captivating physics videos I’ve ever seen:

Each pendulum is at a slightly different length – not just for the visual effect, but it gives them different ~~phases~~periods/frequencies [Seth, the Physicist in Ask a Mathematician/Ask a Physicist wrote me to correct this – Thanks Seth!]

Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion.

For more details see http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pa…

The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations.

This seems easy enough for middle school students to set up and learn from. Our friends at Ask a Mathematician/Ask a Physicist just had a post: Cheap experiments and demonstrations for kids. I think this would be a great addition.

(Via Richard Wiseman)

That is

awesome. Thanks for posting!Stunning.

Very cool! ðŸ˜€

Pingback: Simple, Beautiful Physics: Video Â« Measure of Doubt

This is very, very cool, Jesse.

Is the random motion considered unexplained motion, movement due to external factors (start speed, air pressure, phase of moon, etc…), or something else? I.e., if there were no external influences, would we still observe random motion here?

That is a cool video!

I am unsure, though, about the application of the term “random” to any of the patterns we in the demonstrations. I suspect some of it is because of the way our vision system works – like how a wheel may look like it is spinning in the opposite direction it really is. Since a pendulum’s swing and the rate at which it decreases is deterministic I would guess that high school maths and physics would be capable of saying when you’d get waves, their apparent direction, 2 lines, 3 lines, etc… (but a huge volume of work better suited to computers instead of pencil and paper).

The pendulums represent a function similar to y=sin(x*t), where t is time, x is frequency, and y is position, and as Cory said, your visual system does the work of detecting patterns.

Now, the experiment with synchronizing metronomes shows actual synchronization, and says something fundamental about physics.

The pendulums demonstrate MoirÃ© patterns.

We can see the same patterns by looking at the function y=sin(x*t), where t is time, and x is temporal frequency.

In the pendulum demo, the higher the pendulum hangs, the higher its temporal frequency, x.

If we pause at time, t, we see a wave sin(t*x), where t is the spatial frequency. The spatial frequency increases over time and goes to infinity (picture the wave getting squeezed), but we only have a finite number of pendulums, which represent discrete sampling at certain values of x. Undersampling causes aliasing and MoirÃ© patterns, the same artifacts you see when someone wears a striped shirt on TV.

Ah, so even if there are no external influences, we need to consider the observer’s visual and mental processes. Random enough!

Max, Why the ‘t’ for spatial frequency, isn’t ‘t’ time?

If we freeze the wave y=sin(t*x) at t=2, we get y=sin(2x), so 2 is the spatial frequency.

In the video, x is the vertical axis, y is the horizontal axis, and t is time.

The swinging starts 27 seconds into the video, so call that t=0. If you pause there, you see a line, sin(0*x), which is a wave with zero cycles. Pause 4 seconds later, and you’ll see a wave with one cycle. Pause 4 more seconds later, and you’ll see two cycles, so it takes about 4 seconds for each additional cycle. The most cycles you can see with 15 pendulums is 15/2=7.5 cycles, which takes 4*7.5=30 seconds, and appears 27+30=57 seconds into the video. It looks like two lines, but really those are points on a single wave. It’s the same effect as sampling a sinusoid at its peaks and troughs. Your visual system sees two lines because it likes to pick out lines.

“Random enough”? I still don’t buy that, for if you are suggesting what I think you are, then dependent upon our “mental processes” you and I should start seeing the wheel apparently turning backwards at different forward rates – e.g. you at 30hz and I at 40hz.

On a compute screen, draw multiple radial lines so that you fill a circle but not so close that it’s a solid-coloured circle. You’ll see a moirÃ© that of parabolas that you can figure out the equations for and the stepping coefficient between them. If out mental processes needed to be taken into effect, then the equations and coefficients would be different for you and I – we wouldn’t be seeing the same parabolas.

No only that, but on different days, different mental states, the same wheel would apparent start turning backwards to you at different rotation rates and you’d see different parabolas in the same radial moirÃ©.

Problem is, in both cases, that doesn’t happen. The effects are consistent.

Max: Thks, got it

Cory – Maybe in this case yes, but remember those puzzle pictures in which the object is to pick out a hidden image by focusing the eye just so and from the right distance etc? How do you explain A’s ability to see the large hidden image but not B’s. Failure of some of B’s mental machinery perhaps?

But it does sound like you and I may agree than the word ‘random’ is nonsense. I certainly think so. This word is as bogus as the words ‘time’, ‘movement’, and other commonly used words that we humans use to describe what we experience to each other.

David: no, I’m not sure we do. I’m only disagreeing that in this case “random” is the appropriate word to describe some of the patterns we see in the pendulums. There are still processes out there which are actually random, like nuclear decay, so the term is valid, as are “movement” and “time”.

As for those puzzle pictures you refer to, the ones I’ve seen require you to “defocus” your eyes and then the second image pops out at you through something like pareidolia. Pareidolia is something that I would say is “dependent upon our mental processes” because it is highly suggestible – you can make people see one image or another in a cloudscape by your choice of words. Seeing the wheel apparently rotate backwards, though, is dependent upon the mechanics of our visions system and how fast we can process new images.

Random means it can’t be predicted, but the patterns we’re talking about are easy to predict. Just sample a function like y=sin(pi/2*t*x) at x=0, 1/15, 2/15, 3/15… 15/15.

We can model some non-random functions as random. For example pseudorandom numbers are predictable if you know the function and the first number, or the seed, but they look random enough.

Pingback: Synching Up: Another Cool Physics Video « Measure of Doubt