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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I wonder, can this be achieved by a particular non-uniform gravitational field?
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The eom is something like m a(t) = F_G sin(phi) So if you have a gravitational potential F_G = mg phi/sin(phi) You should get harmonic oscillations for all phi (no Taylor expansion needed)
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