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Galileo's pendulum

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Galileo's pendulum

Old 21st Feb 2015, 23:00
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Galileo's pendulum

Just been watching a TV programme on the history of timekeeping. It restated the so often told story of Galileo's observation of a swinging suspended lamp; he noticed its periodicity was constant, and then proved this with a series of unstated experiments.

What I want to know is how did he notice this in the first place? And then how did he prove it?

The only true timepieces available were sundials or shadow clocks; water clocks or sand glasses could measure elapsed time to some extent, as could a burning candle, but how could you use any of these to prove, or even detect, constant periodicity of a pendulum.

Anyway, it's probably time I went to bed.
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Old 21st Feb 2015, 23:05
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As the swinging lamp was, in fact, a chandelier (in Pisa Cathedral), he might have just 'counted' - and noticed that, regardless of amplitude, the time taken was constant.

Galileo discovered the crucial property that makes pendulums useful as timekeepers, called isochronism; the period of the pendulum is approximately independent of the amplitude or width of the swing.
From:- http://en.wikipedia.org/wiki/Pendulu...o.27s_research
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Old 21st Feb 2015, 23:13
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But that doesn't prove anything; how did he know his count was constant and equal, the same applies to breaths or heartbeats?

I'm not being difficult here, I think it's something we've all just accepted without questioning for, well, a long time...
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Old 21st Feb 2015, 23:18
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By remarking that the swinging lamp was a large chandelier, I assumed (but didn't remark) that the period would be quite 'long' - therefore relatively easy to 'time' by counting (rather than a short 'clock' pendulum - which would be quite quick).
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Old 21st Feb 2015, 23:23
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one over 2 pi times the root of l over g to a close approximation. Mass doesn't enter into it.

After etc...
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Old 21st Feb 2015, 23:24
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Indeed, henry, that's what the nice but dim bloke in the program said. BUT FOR ****'s sake. What a bizarre load of total bollox mixed with simplistic tat, overlaid with a sickening noise labeled as music background.

Phew, got that orf me chest.


It was thought that Galileo's father, a musician, taught his son such exact timing that he could time his experiments in his mind alone. Remember, dropping things off the Leaning Tower probably did not happen - apart from a public display or two - but timing balls running down curved troughs probably was the way it was done. That probably word keeps cropping up.

One and two and three and . . . Dad could better a candle anytime.

Vincenzo, in his study of pitch and string tension, produced perhaps the first non-linear mathematical description of a natural phenomenon known to history.[1] This was an extension of a Pythagorean tradition, but went beyond it. Many scholars credit him with directing the activity of his son away from pure, abstract mathematics and towards experimentation using mathematical quantitative description of the results – a direction which was of utmost importance for the history of physics, and natural science in general.


https://www.google.co.uk/search?q=vi...alilei&spell=1



Oh, by the way, since it doesn't matter anymore. My space ship in The Perfect Code was named after Galileo's daughter. A big thanks to Dava Sobel who left me intrigued with the mystery of Galileo's missing letters.


http://www.mcgoodwin.net/pages/other...odaughter.html


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Old 21st Feb 2015, 23:30
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Sorry guys, but your pulse isn't constant, neither is a count.

Yes, a large period of swing might help, but using the tools available, I don't see how you can prove anything.

If you had a second, exactly equal length and mass, pendulum you might be getting somewhere, but it's swing length would decay at the same rate as the subject, so you still can't really say you've done anything other than saying, "well it feels about the same length of time, so it must be"
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Old 21st Feb 2015, 23:31
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Mass doesn't enter into it.
No, but length does, and a large chandelier would be long.

it's swing length would decay at the same rate as the subject, so you still can't really say you've done anything other than saying, "well it feels about the same length of time, so it must be"
The point is that the time taken is the same - regardless of the amplitude of the swing (at least at small amplitudes).

Galileo was moved to investigate the phenomenon having noticed the equal time period.
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Old 21st Feb 2015, 23:41
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No, no , no, you can't time balls running down a curved trough, (beautiful image though it is), because you've got nothing to time them with, to confirm a constant transit.

You are all assuming a means of measurement, which itself cannot be measured as constant or consistent.

I like the idea of training someone to "perfect timing" but it still doesn't actually prove anything.
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Old 21st Feb 2015, 23:53
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ssb-

Easy peasy. Once the apparent variables are worked out (hmmm... seems that two pendula of identical length seem to have the same period. Let me test this...)

One tests this timing hypothesis by one of two ways:

1) Start two swinging simultaneously but with different amplitude.

2) Start one swinging, let it decay for a time, then start another.

If you've hit upon the appropriate variable or combination of variables, they should remain synchronized.

Of course, that's for your hypothetical pendulum. Your chandelier or censer or whatever introduces friction, air resistance, possible added forces, etc. into the mix. One suspects that over short periods, a keen observer might suspect that synchronizing these things might appear simple, but as the time of observation increases, errors start appearing due various factors.
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Old 21st Feb 2015, 23:55
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Yeah; but I think that the honest burghers of Piza Cathedral might have a word or two to say about that.

You're probably right though.
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Old 21st Feb 2015, 23:56
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Well, it was about as good as it got in those days, and remember, you're dealing with the minds of a geniuses. They wouldn't be fooled by simplistic side effects.


Curved troughs? That's exactly what Galileo used. And yes, he adjusted for the curves.


John Gribben. But he's written so much I can't find the specific subject in this forum timescale.
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Old 22nd Feb 2015, 00:26
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I agree with Henry.
All the evidence I'm aware of is that he used his pulse to time the pendulum swings. And if you've spend as long as he or I have in Cathedrals, you'll be aware that there's sod-all else to do as a scientist but look for patterns in the phenomena around you.

From the initial observation,with (inaccurate) pulses to give one the idea, one can then do matched experiments back home which develop the theory.

The timing troughs are in the Galileo museum in Florence, quite near the Uffizi (it's well worth a visit if you're in town). The balls rolling down trigger bells. The human sense of rhythm allows the bells to be spaced so that they are triggered at equal time intervals. I have replicated this in the school physics lab, and it's remarkably easy to be very accurate. What one cannot tell is how long the time interval is against the modern second, but this is not important for proving the theory.
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Old 22nd Feb 2015, 02:22
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If the subject was a chandallier: Before electric light, those things was hanging in a crane mechanism to either lower to ground-level or rise to above loft-height where the candles or oil-lamps were lighted.
A chandallier in swing during this movement will change frequency remarkable enough to percieve it without time measuring. Once have had this experience, it's easy to compare two Chandalliers/pendulums side-by-side and start counting how many swings it demands to swing parallel again - quite like comparing Your cars turn signal with the one on the car in front of You: At some time they will blink at same moment whereafter they will differ for a time!

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Old 22nd Feb 2015, 03:46
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My empirical evidence proves that its always a sunny day when stuck in a church. I would imagine the same to be true for Galileo.

So he could just have watched the Sun's shadow passing whole tiles or bricks and applied some trig if necessary. He might have used candles, but by arranging them in an arc at equal spacing or at proportional spacings in a straight line he wouldn't need to have lit them.
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Old 22nd Feb 2015, 08:14
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Thank you gentlemen; I think that's another little mystery solved.

Personally I'm inclined towards the balls in a trough solution; although I suppose you could equally allow your balls to fall through a cylinder of honey, or perhaps have a friend drop then from a great height.

As an old instructor of mine once said about a fellow student, "give this man the job, and he'll finish the tools!".
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Old 22nd Feb 2015, 08:17
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Just because we now have very sophisticated time pieces and other equipment does not mean that we can discredit the abilities of previous generations. The Antikythera mechanism was made without the CNC lathes and milling machines which we would regard as vital to make such a fiendishly clever device.

The pulse varies slightly, but over the course of several observations a reasonably accurate average figure can be arrived at.

In the 1970s I saw an Open University programme about Galilleo and it showed the device he made for studying acceleration. I adapted it, added a chain and handle and chicks to make it into a mechanical toy, Gallinae Priemis (Spring Chickens)


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Old 22nd Feb 2015, 08:36
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To get back to that documentary,it appeared to be aimed at a audience of ten year olds,throwing in clips from cartoons and various other ruses and witticisms to keep the kiddies amused,more Channel Five or CBBC than BBC.
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Old 22nd Feb 2015, 09:28
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It's a good job I didn't view it then - way above my mental level.
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Old 22nd Feb 2015, 09:32
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Way back when I used to develop & print all my b&w 35mm stuff I found that I could eventually count up to 2 minutes or more just as accurately as a digital timer.

Always wondered after that how humans could measure time so accurately, but there is no doubt that it is possible.
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