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Huygens' Clock Puzzle Solved
PhotoGuy writes "Okay, I haven't heard of this puzzle either until now, but it sounds like a fascinating phenomenon. According to this article:Huygens had two clocks side by side and he found that even when they began out of sync, they soon got into a rhythm where the pendulum on one moved as if it were a mirror image of the other.The article is pretty light on the explanation, noting only the conditions required (small relative mass of the pendulums [pendula?], relatively close speed of the clocks), and not really addressing the physics behind it.
" There's a great site at Georgia Tech that explains the puzzle in more detail.
[quote]The combined mass of the pendulums has to be very small compared to the combined mass of the entire clock assembly and frame - this was where Huygens was lucky. [/quote] i'm not sure where non linear dynamics and chaos theory come into this, but ah well... i probably wouldn't understand it, anyways. so... that which intrigues man has gone from undiscovered land masses, to redisocvered lost cities, and now to ancient riddles. i wonder what we're going to do for intrigue once we solve all these ancient riddles...
Strangely enough, it didn't occur to them to test what happens if they put three clocks side by side... Antiphase synchronization seems somewhat hard with an odd number of clocks...
Say no to software patents.
When I was looking at this I was expecting something filled with tons of wizzbang scientific explainations. Sad that something that has stumped people since the 17th century turns out to be primarily luck.
( o ) one could say I'm rather baked
From the Article:
>
As Huygens surmised, the platform motion is the culprit: if we prevent the platform from moving, there is no synchronization at all
Can you believe it took this long to solve this problem? I admit I'm sceptical. Am I missing something?
Here's how I interpret the phenomenon:
Imagine two pendulums hanging side by side (on a rocking boat (I tried to make ASCii art, but the lameness filters don't like whitespace) Align the pendulums so that they swing in the direction of the boat rocking side to side.
Pull the pendulums apart and release simultaneously (assume they don't collide).
Initially they are 180 degrees out of phase, but as the boat starts rocking, its like giving one an extra push (in phase), while the other (out of phase) pendulum a tug to shift its sinewave in the opposite direction. Eventually both pendulums will have the same phase shift and will be affected by the rocking boat equally.
A slightly more complicated example could include two children on a swingset put into phase by giving each a strategically timed push or by loosely comparing it to the harmonics that caused the destruction of the Tacoma Narrows Bridge in those old film clips.
Sounds more like vibes 101 problem than a 336 year old unsolved problem.
Am I overlooking something?
The first time I heard of this was in a book called _Drumming at the Edge of Magic_, written by former Greatful Dead drummer Mickey Hart.
He was discussing the pervasiveness of rhythm, and used this as an example.
Of course, he didn't try to explain the science, and I wondered why at the time.
Writers imply. Readers infer.
If anyone is interested in accuracy in time keeping, a trip to the Royal Observatory in Grenwich is a must for you. You can see Huygens' parabolic pendulum located there.
Get to know about John Harrison, who made the first 'accurate' timekeeper, for use at sea to measure longitude. See Harrisons first accurate time peices of the world, H1 thru H4, where H1-H3 still ticks today.
A must is to stand on the prime meridian of the world, which represents 0 degree longitude, also located there. At night, a green laser can be seen streaking across the sky marking the zero parallel.
Check out the Royal Observatory, you won't regret it!
I would say the simple solution is gravity, plain and simple.
You have two masses moving, in essence, side to side (horizontally).
X
The masses are equal, but not perfectly in sync. It's pretty impossible to get anything perfectly in sync. So basically, sooner or later, they will both reach the center point X at the same time. When they do, the gravitational attraction between the two masses is at it's highest. When the pendulums begin to move apart again, they are affected by an equal force resisting them moving apart. Regardless of their acceleration away from each other, they will from this point forward always come to the center point at the same time, because that is where they "want" to be.
If you want to wax intellectually on the subject, we can take a look at the clocks themselves.
As each pendulum swings, it imparts a torque on each clock. When the pendulums meet in the middle as I've described above, the torque on each clock is exactly equal and opposite also. Assuming the clocks are equal in mass they will fall back like little pendulums themselves, but at the same rate.
So what we have, basically, is gravity multiplying itself harmonically. Fascinating.
Bah.
Cool! Amazing Toys.
No, simple linear dynamics won't help you (and if they work out with your perl-script, then probably because of nonlinearities creeping in due to rounding). That is, because you can only get linear behaviour out of a linear system. That means a linear system can be described by a matrix, and the eigenvalues of that matrix will give you the frequencies of oscillations that may happen (given the System oscillates about a stable state). If you couple linear systems in a linear fashion (like with a force k(x1-x2) as you suppose) you only get a bigger linear system, with more oscillation modes.
In a purely linear system all these modes of oscillation are independent of each other. But the clocks manage to get from one mode of oscillation into another. This can only happen, if energy is somehow transferred between the modes, and to get that you need a (nonlinear, or you get just another linear system with slightly different modes) coupling between the modes.
Linear Systems are, in a sense, boring, once you have worked out all the coupling constants, put them in a matrix and found it's eigenvalues you know all about it (for large enough systems, say a crystall with 10^23 Atoms that can be quite a feat and can get you some interesting results nevertheless) and can predict it into all eternity. The interesting stuff happens when nonlinearities creep in.
You could describe our solar system in a linear manner, and you will learn much about it by that, mainly that the planets orbit about the sun and are themselves orbited by moons. But if you want to know why some orbits more stable than others, for example why there are gaps in the saturn rings for orbits in sync (with w being a multiple of the W of the moon) with the moons, you have to look into the nonlinearities.
--
"By the way if anyone here is in advertising or marketing... kill yourself." -- Bill Hicks
In a piano, some of the keys strike a pair (or three) strings when struck. Piano tuners tune each of the strings independently, but also realize that one string affects its mate. Even if they are tuned just a titch off from one another, they will try to sycnh up. Instead of seeking to tune the pair perfectly together, detuning one from the other very slightly will affect the loger-term 'envelope" of the note.
Could the pendulums be iron ferrite or have trace elements of magnetic metals?
This must be Thursday, I never could get the hang of Thursdays.
Unfortunately, the Royal Observatory has gone a little soft in the science in the attempt to attract tourists. It's not quite as bad as Disney, but it's definitely enough that people who actually care about this stuff will go quietly mad. (Disclaimer: the following comments are based on reports I've seen in various locations over the past few years - it's possible they finally got their act together.)
The most obvious to most people is the fact that a GPS shows that the PM is marked by an unlabeled garbage can (read: ignored) while the PM marker is a substantial distance off - as much as 100m?.
There's actually an easy and fascinating explanation. Geographical positions were originally determined by astronomy, and this implicitly took into account the actual complex shape of the earth. Most slashdot readers know about the equatorial bulge, but there are other bumps and valleys as well. But modern positioning uses GPS and a simplified model of the earth's shape, and the coordinates do not match exactly. Minimizing the differences worldwide required a sizeable jump in the London area.
This then brings up the difference between astronomical time and atomic time, how GMT tracks the former and UTC tracks the latter, and the need for leap seasons.
I think it's reasonable to expect anyone who knows enough science to visit the RO would find this interesting, but the RO apparently doesn't. Most people think the positioning of a garbage can on the true PM was an accident, I'm not so sure.
Even more bizarre was their behavior around January 1st, 2000. It wasn't Y2K until it was Y2K in London. Except it was. Except it wasn't. I don't think anyone ever figured out what their position was, except that all celebrations should somehow refer to them. (It got so bad I half expected to see a claim that the RO patented Y2K.)
Ironically, I never heard of any reference to the reason why this time zone was first among equals - the fact that UTC is widely used in computers, telecommunications, etc. Half of the world (by definitition!) may have been in 2000 by the time it hit midnight in London, but much of the technology of the world would turn over at that time. That's why I was glued to the TV at 5 pm local time, with CNN on one TV and BBC America on another.
If you have a chance to visit the RO, take it. But think of it as "Royal Observatory World," the theme park.
For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken