Can a swinging pendulum reveal that the Earth turns — without ever looking at the sky?
▶ Launch the interactive simulationIntegrate the rotating-frame 2-D oscillator with energy-conserving RK4 at latitude φ; at each turning point record the swing-line azimuth, least-squares fit azimuth against time, and compare the fitted precession rate to Ω·sin φ. The 'day' is sped up so the rosette precesses in ~1 minute. ?lat=<deg> sets the latitude.
the swing plane PRECESSES at the rate Ω·sin φ — a full turn per sidereal day at the pole, none at the equator — so the slow rotation of the swing line is the ground (the Earth) turning beneath the pendulum, exactly as Foucault demonstrated in 1851. The measured rate matches Ω·sin φ to 0.00% at 90°, 45°, 30° and 0°.