Slashdot Mirror
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.
The GA tech column had an link to a picture of the wired article about it, I dug into Wired and found the text so it's more readable.. the link is: http://www.wired.com/wired/archive/9.03/eword.html ?pg=6
http://www.sciencenews.org/20001007/mathtrek.asp
It seems that the main reason this happens is that the synchronus movement causes less vibration in the system as a whole, and therefore conserves more energy. A path-of-least-resistance sort of thing.
Perhaps there's a physics major out there who could explain better...
I'm interested to see if this may lead to a better understanding of how harmonics works with relation to high-rise buildings. Particularly in earthquake country. (see this)
We've got buildings that can withstand strong quakes -- but not necessarily those of long duration. I'll bet a shiny new penny that this reseach may be insightful in this field.
-jhon
Not so. The three would each be off by 1/3 of a period.
Just like three phase power... three sine waves 120 degrees apart. Sum them and you have a constant 0.
I've no idea if that would actually happen in that setup, but my guess would be that yes, they would cancel each other out in total antiphase this way.
That's called the Harem effect (or something like that). Basically you get any number of women, greater than 1, put them into close contact with each other and they all have their period at the (nearly) same time. Well documented phenomeon(sp?).
Harem, because a man could impregnate his entire Harem in a single day since they all became fertile on the same day.
It's a very difficult problem to model. It involves two pendulums (both of which, despite what many of your freshmen physics professors told you, are nonlinear oscillators), and a coupling mass.
The coupled oscillators are difficult enough to model by themselves. I wrote a paper once on coupled physical pendulums. After quite a bit of very complicated physics involving Hamiltonians and Lagrangians and other silly names, I managed to derive an equation that describes the motion of the two pendulums in terms of the 'normal modes' of oscillation (these are closely related to the 'in phase' and 'out of phase' vibrations). Needless to say, the equation took up a good 3 lines in the report. I should have just put it in an appendix.
Now if you add a coupling mass between them, you're talking about an even MORE complicated problem, because the inertia of the coupling platform affects the resonance of the pendulums. It's very much like an inductor in electronics. It doesn't allow energy transfer to happen directly through the two pendulums, because a pendulum has to push the whole mass in order to get energy over to the other pendulum. I would imagine, just through experience in nonlinear systems, that increasing and decreasing this mass will have yet more nonlinear effects on the system (such as the complete stopping of one pendulum, although the article was unclear as to whether this was a complete halt, or just momentary).
You'll find very little chaos in this system, unless the pendulums are started at a very large height. Also, like most undergraduate physics, this analysis completely ignores the effects of friction, which is where the only true energy 'loss' would happen.
Mod this down for overkill,
~Loren
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!
Harem, because a man could impregnate his entire Harem in a single day since they all became fertile on the same day.
More likely because a harem would be an environment in which many women lived together without much contact with the outside world.
I mean, some of these sheiks were reputed to have dozens of women in their harems. No way he could impregate them all on the same day , at least not with the technology that existed at the time.
Nowadays, for that sort of thing, we have Cowboy Neal...
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
You get it with piano strings too. Where two or more are tuned to the same note. The delta in tuning has an important on the sustain-decay profile of the notes.
Huygens figured out the general principle. If you have two things that are matched in frequency, and capable of influencing each other, then any influence, however tiny, will eventually drag them into some preferred phase relationship. If there is some difference in frequency, then this may destroy the coupling effect, if it is too small. You get it with piano strings too. Where two or more are tuned to the same note. The delta in tuning has an important on the sustain-decay profile of the notes. Arguing that entrainment must exist to some degree between two clocks is easy. Showing exactly what causes it is a lot harder. That is what the recent paper was about.
Not really, Although you have a valid point, the article specifically states that the effect only worked on smaller weighted pendulums - larger ones would have a stronger gravitational effect. On top of this, if both pendulums were started in the same direction, then they would not be moving away from each other and thus the gravitational effects on each other would be unchanging. Thus gravitational effect would have no bearing at all. In the article at Science News (http://www.sciencenews.org/20001007/mathtrek.asp) they specifically mention that the pendulums were started in opposite directions, and also in the same direction.
Sounds like a great premise for a Fox reality game show.
the decades old question of why Guinness bubbles 'float' down the glass has been solved. Actually took some high end fluid modelling software to figure it out :)1 31010,00.html
http://articles.thetechmag.com/articles/?0,0372,0
Also a press release here: http://www.fluent.com/about/news/pr/pr5.htm