Simple Pendulum

A rigid simple pendulum with adjustable length, gravity, and damping. Compare small-angle harmonic motion with larger amplitudes where the period depends on amplitude.

Who it's for: Waves and mechanics courses; demos of periodic motion and damping.

Key terms

  • pendulum
  • period
  • small-angle approximation
  • angular frequency
  • damping

Live graphs

How it works

A simple pendulum obeys nonlinear equation θ¨ + (g/L)sinθ = 0. For small angles, sinθ ≈ θ and the motion is simple harmonic with period T ≈ 2π√(L/g). Larger angles increase the period. Damping removes energy over time.

Key equations

Equation of motion:θ¨ + (g/L) sin θ = 0
Small-angle period:T₀ = 2π√(L/g)
Larger amplitudes: period increases; the sidebar uses T ≈ T₀(1 + θ₀²/16 + 11θ₀⁴/3072) with θ₀ in rad (undamped).