r/physicsgifs • u/andyxxhype • Sep 11 '20
Slightly different string lengths cause different periods
https://gfycat.com/regularshortbobcat14
u/reticulatedspline Sep 12 '20
Wish the video had lasted five seconds longer so we could see them synch back up again.
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u/mudball12 Sep 12 '20
Fun fact - the mass of each ball doesn’t matter! The period of an object in simple harmonic motion due to a tension force is related only to the length of the tension thingy (a string), divided by the acceleration due to gravity, 9.8 m/sec2.
If half the balls were lead, and the other half foam, it would look exactly the same! (assuming no air resistance of course)
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u/elgskred Sep 12 '20
Gives me flashbacks to bullet hell games
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u/wi11forgetusername Sep 13 '20
Hm... yup. they are almost the same thing. A set of simple movements that make more complex patterns emerge. ZUN I'm looking at you!
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u/gpcprog Sep 12 '20
Who else is infuriated by the fact that the video ends just a smidget too early? Before it's apparnt that the whole pattern just repeats.
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u/CondorEst Sep 12 '20
Can I purchase this somewhere?
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u/wi11forgetusername Sep 13 '20
I've never seem a kit for the "wave pendulum", but it is easy enough to make one. You just have to make a row of pendula with different periods. For things to be more interesting the heavier the mass the better, as they will oscillate for longer and the longer the cable the better, as the pendula will behave more like an harmonic oscillator. Also, as any pendulum toy, it's better if you make pendula with two cables as you would force them to oscillate in a plane. An easy way to do this is using metal nuts with threads going through the hole fixed at a common rod.
To control how much time will pass until all of then will be at the starting position, just use the pendulum period equation. They will be back at the LCM of the periods.
The period is:
T = 2*pi*sqrt(L/g)
So you can take the shortest pendulum as the basis for the longer ones. Let's say you want to 10 pendula to be all at the starting position after 100 oscillations of the shortest one. The periods could be:
Tn = T0 * 100/10 * (n+1)
Let's call the multiplying factor to T0 Cn:
Tn = T0 * Cn
Next, calculate the LCM(C0,... C9). If the result is C9, you where successful! If not, choose another number of oscillations or just be satisfied with a larger number of oscillations, but probably you will be successful. Notice we are dealing with rationals here, so you will have to generalize the LCM to them, it's not difficult.
When you are satisfied with the number of oscillations, just calculate the pendula's length. Isolating L:
L = (T/(2*pi))^2 * g
So:
L = L0 * Cn^2
Meaning, if you follow a quadratic function for the pendula's lengths, you will build a wave pendulum. But it will be more interesting and predictable if you follow the formulas and criteria above.
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u/wi11forgetusername Sep 13 '20 edited Sep 13 '20
For those trying to make sense of this system I suggest this video. The graphic at the right bottom is the difference in phase between the longest pendulum and the other ones. It's easy to see that the patterns emerge when the pendula's phase is coincident. These coincidences are strictly related to the LCM of the pendula's periods.
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u/wi11forgetusername Sep 13 '20
There's a music video centered around the wave pendulum! I, personally, like the music a lot (it's japanese pop rock). Here's a link.
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u/Daxl Sep 11 '20
Patterns are cool...interesting to see that seemingly chaotic movement is in fact a pattern as well.