Ladder

Pendulum — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. −π−π/2π/2π-22angleangular velocityat rest, hanging downbalanced upside downclosed: swingingopen: going over the topdashed: the boundary

    The pendulum, and the small lie that makes it simple

    A pendulum's period does not depend on how far it swings. This is one of the most useful false statements in physics, and it is worth knowing exactly how false.

    rung 1 · mechanics
  2. 02040608010012014016011.21.41.61.822.22.4amplitude (degrees)period ÷ small-angle period23° : 1.01090° : 1.180the small-angle formulathe θ²/16 correction

    The period that depends on the swing, computed exactly

    A pendulum's period is not independent of amplitude. The exact answer is an elliptic integral, it has no elementary form, and plotting it shows precisely where the famous approximation earns its keep and where it collapses.

    rung 2 · mechanics

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