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, Reply)
