Fun watching pendulums

[BobSch]

Doesn't take much to keep me occupied.

http://sciencedemonstrations.fas.har...econtent341734

[paultnl]

wow

Fascinating, I am tempted to build one

[jking]

Very cool.

[LCHIEN]

Just had to go thru the thought process of how to build this guy.

the hard part of this will be tuning the 15 individual pendulums so they have a period within about a percent of the prescribed frequency (51 cycle /minute to 65 cycles per minute). The period is 1/frequency (in this case with a unit of minutes)

Pendulum periods are T=2 x sqrt(L), L being the length of the pendulum in meters and T being the period in seconds (so you need to convert to minutes). Its a function of gravity (which on the surface of the earth is a constant). The mass of the weight is not really consequential but you have to have a large percentage (like 99%) of the moving weight of the whole pendulum in the weight so that the weight of the string distributed along the length of L rather than at the end is small.

So to build this there is a limited number of calculations to be done for L and then you have to (and this is the critical part) trim the suspensions to around about a percent accuracy of the calculated length. The suspension top is not critical (I'd build it out of wood) it should be stiff enough not to flex and tall enough for the computed length of the pendulums.

just ran thru the calculations, the pendulum lengths would be about 8 to 14 inches and an adjustment accuracy of about a 1/8th of an inch would be about 1% in period error. So that's actually pretty easy.

[jnesmith]

Build me one too.

[cabinetman]

It doesn't appear that there's that much precision to length. It may be in the suspension design (not a single line), and each one is in the same progressive length to the next longer one. It would be fun to experiment making one.

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[LCHIEN]

thinking about it some more, each pendulum is about 1.5% in frequency or period from the next one. An accuracy of 1% in the pendulum frequency is probably therefore not good enough. if you want them to line up properly after a minutes free-swinging.

I'm thinking probably ~1/10% is probably required.

[Alex Franke]

The referenced AIP article shows and describes each of the 1/2" diameter brass bobs as being attached with a single strand (unlike in the video) through a hole at the top to a thumbscrew, which is used to fine-tune it.

I suppose you could use the same technique the way the bobs are attached in the video, but you'd have to figure out a way to avoid twisting the line. With only a single line, I think it would be trickier to get started straight...

[Alex Franke]

The lengths of the pendula, by the way, are "adjusted such that the longest pendulum executes L oscillations in a time interval T, then each successively shorter pendulum will execute one additional oscillation in that same time interval."

[LCHIEN]

there are at least two ways of making an adjustable length - one is to have a hanger loop or eye on the weight and have it threaded into the bob. If you use a 6-32 thread then each turn of the bob would give you 1/32" adjustment, you could easily do 1/4 or 1/2 of a turn.

You could have the end of a doubled-wire; one end-adjusted would give you twice the sensitivity. Also having a doubled line as shown in the vid keeps the pendulum swinging primarily in one plane, I think an advantage.

Tuning it would be a chore, each pendulum would have to be tuned and take a minute or more for each iteration, several iterations would be required. Could be hours of work.

At the end of the video, when they all return to being in a line, you can see the second to last of the far-end bobs not quite lining up... that's the result of not being quite tuned perfectly.

I'm trying to think of a way to accurately set the lengths and then assemble it without tuning, but, like a guitar or piano, tuning may be a requirement. The periods being so long makes the tuning slow.

[cabinetman]

If I make one I'll keep ya posted on how it goes.

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[Mr__Bill]

It's fascinating, thanks for the link. I'll likely not get anything else done today just browsing the site looking for more of the same.


Bill
on the Sunny Oregon Coast

[Alex Franke]

I don't want to hijack this thread or anything, but in the spirit of "more of the same [fascinating stuff]" I thought I'd post this little gem: http://www.youtube.com/watch?v=Ws6AAhTw7RA

Now back to the pendulum... I like the double-line idea, too, because it makes it easier to swing the bob straight, and has the side effect of doubling the fine-tuning precision. But how would you attach the line to the thumbscrew so that it didn't twist? I can't imagine a lot of twists would be very good, but maybe it wouldn't matter at all...

Also, I bet you could nail down the tuning a bit by recording the period at the first setting, turning the thumbscrew a precise number of times, recording the period at a second setting, and then doing a little math to see how much it needs to be turned again...

[BobSch]

Man, if I'd know this thread would have involved math I never would have posted it!

[gsmittle]

Man, if I'd know this thread would have involved math I never would have posted it!

Hear, hear! All you engineering types are making my brain hurt.

g.