I knew about it being true for small angles only, but I just realized that I don’t know why. Is it related to the ratio of the mass of the weight to the mass of the rod or string?
We teach the youth that the period of a pendulum is independent of its amplitude •This isn't quite true. It's only true for 𝑠𝑚𝑎𝑙𝑙 angles θ •In reality, a pendulum's period is only independent of its amplitude if it moves along a cycloidpic.twitter.com/0si5dAcAuV
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it's because the small angle approximation neglects the higher order terms in the initial angle θ
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Here's an easy way to understand why the period diverges as the angle increases: just imagine dropping the pendulum from an almost vertical angle. It can take a long time for it to go down on each swing, as it almost balances at every high point. (On top, the phase diagram.)pic.twitter.com/GYRSlCBDze
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I'm not gonna lie, your animations were the first to get me interested in animating
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does this completely match with the small angle angle approximation?
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yup! you can see it in the smallest oscillation
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I wonder, can this be achieved by a particular non-uniform gravitational field?
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that's a fun question .. i would imagine so but i'm not sure
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Maybe we should have given our 7th Leiden
#wallformula a smaller amplitude
. Still, ... we love it like this. @sensemolen@TEGENBEELD#Huygens https://muurformules.nl/ pic.twitter.com/bQQc6WWekJ
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When teaching differential equations, I had a student invent a decent chunk of the theory of the Jacobi Elliptic functions because they were dissatisfied with the small angle approximation
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Husband Physics Professor in a small college says he specifically does NOT teach that!
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