do they have to be equally spaced,
the lengths of the string? like 10,11,12,13 cm, or can you just do any old increasing lengths and get the same results?
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JeremyBeadlesHands, Sat 6 Apr 2013, 21:15,
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you'll get the best result
if they're evenly spaced, but you'll get similar results if you're a bit random wit the lengths
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LP, Sat 6 Apr 2013, 21:28,
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The lengths are important
With the weights being equal the length of the string is the only thing determining the periods of the pendulums. The frequency goes as the square root of the length of the string*, so it's not as simple as making each one a cm shorter than the previous one. If you did that I don't think you'd see any pretty patterns.
Look here for some example lengths.
ω=√(g/l) where g = 9.81 m/s^2 and l is the length, just in case you were wondering. The period is 2π√(l/g).
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jonbob loves you, Sat 6 Apr 2013, 21:37,
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Nothing as fancy as maths.
Just first year mechanics really.
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jonbob loves you, Sat 6 Apr 2013, 22:05,
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good work
that contains the best idea too - make them adjustable so you can fine tune them
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JeremyBeadlesHands, Sat 6 Apr 2013, 21:45,
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I just drew a diagonal line
and made the pendulums fit the line.
Worked fine :)
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LP, Sat 6 Apr 2013, 21:51,
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Hmmm. Posting equations on the internet on a saturday night?
I'm guessing you're not currently fighting off the amorous advances of Mr Right? ;)
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Tab Hunter Make this useless process end and so, begin again, Sat 6 Apr 2013, 22:05,
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That's up to you...
...assuming I'm forgiven for the bearded ginger comment.
edit:this is true, by the way, although something tells me I'm sort of sabotaging my own position by digging out old SMBC comics on a Saturday night.
Hang on... what the hell are you doing here?!
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jonbob loves you, Sat 6 Apr 2013, 22:07,
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I am currently in the doghouse for "popping out for a pint" till four this morning.
And so am staying in & playing drums. Badly.
You are forgiven for the bearded ginger comment. You terrible person, you.
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Tab Hunter Make this useless process end and so, begin again, Sat 6 Apr 2013, 22:25,
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Nothing wrong with being a bearded ginger.
They're just the sort I go for. God help them if they're into science too.
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jonbob loves you, Sat 6 Apr 2013, 22:31,
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talking of guys who like ginger sciency guys
I've just remembered I was supposed to be going to my mates birthday party tonight.
Bugger.
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LP, Sat 6 Apr 2013, 22:47,
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He won't mind.
Just have a whole birthday cake to yourself, drink a couple of bottles of wine and spew it all up on the carpet (filming it all in portrait).
Then send him the video. Apology will be accepted, I'm sure.
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MyFrontFellOff ; his mouth full of teddies, urinating defiantly, Sat 6 Apr 2013, 22:57,
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F.R.E.A.K.
Here, go wank your cock off.
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Tab Hunter Make this useless process end and so, begin again, Sat 6 Apr 2013, 23:43,
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Sorry for nerding out but I LITERALLY CANNOT RESIST.
I made this with some 2p coins, piece of wood and some fishing wire and blu-tack.
Off the top of my head, so prone to error, but will give you the right idea hopefully:
You need to choose lengths such that each (for example) pendulum 0 completes N oscillation when pendulum 1 completes N+1 oscillations and in the same time pendulum 2 completes N+2 oscillations.
This way they will all eventually 'meet up' again at the end of the time it takes for pendulum 1 to have completed it's N oscillations. In between that, what you're seeing is a 'wave' of gradually increasing frequency as they gradually go out of sync by amounts proportional to their periods. In the parts where it looks like they're going random and mental, they're not - they're just 'waving' at a frequency that's too high to be sampled by the discrete number of pendulums - i.e. you're seeing what it looks like if you try to draw a very wavy wave with only a few 'points' (pendulums). You don't have enough points to fill in all the details and it looks like you're just getting random points. Like join the dots before you've joined the dots.
Anyway, I digress, to find the lengths that you should use, employ the equation for period of a pendulum: T= 2*pi*sqrt(L/g), where L is length of pendulum and g=9.81 is a constant representing the pull of gravity. You want to require that pendulum 0 will do N oscillations in some time T_total. So the period of pendulum 0 must be T_0=T_total/N. Then require that pendulum 1 does N+1 oscillations in this same time, so that T_1 = T_total/(N+1). In general, for the ith pendulum you'll require that T_i = T_total/(N+i).
So if you choose T_total (How long you want the whole thing to take to repeat - I think I remember that 30s was good for me since my pendulums were quite heavily damped, so they slowed quite quick), then you can get values for all the T_i, and then re-arrange T_i = 2*pi*sqrt(L_i/g) to get all your lengths.
Just realised that I said my pendulums are quite heavily damped. Nice.
(, Sun 7 Apr 2013, 0:03, Share, Reply)