Sandbox
When does the textbook stop being true?
Every textbook says a pendulum's swing time is 2π√(L/g). That only works for small swings. The blue ghost follows that shortcut; the yellow bob follows the real equation. Pull it out wide and watch them split.
About this sandbox
A pendulum swinging next to the textbook small-angle shortcut, T = 2π√(L/g). On small swings they match; on big ones the real pendulum falls behind, and the page shows by how much.
Things to try
- Release it at 10°, then at 150°.
- Take it to the Moon or Jupiter.
- Add air drag and watch the swing die away.
More in Swings and wobbles: Spring, Double pendulum. See every sandbox, or type your own equation in Free mode.