Pendulum period simulator
For a simple pendulum at small angles, the period is approximately T = 2π√(L/g). Doubling the length increases the period by √2 rather than doubling it. At larger angles the small-angle formula becomes less accurate.
A simple pendulum
The small-angle approximation predicts a longer period for a longer pendulum. The simulation integrates the nonlinear equation with damping.
T ≈ 2π√(L/g)Small-angle period: 2.37 seconds.
OpenStax · Pendulums ↗These are numerical illustrations. Exported values are simulation data, separate from the published human-study data in the research library.
Try this
Move the length control from one metre to two metres. Compare the displayed small-angle prediction with the slower swing. Export the numerical trace to inspect angle and angular velocity.
What the model leaves out
The animation integrates the nonlinear damped equation using RK4. The period label is a small-angle approximation. The model omits air flow, pivot friction models, and flexible suspension.
Where the equation comes from
The small-angle approximation predicts a longer period for a longer pendulum. The simulation integrates the nonlinear equation with damping.
OpenStax · Pendulums ↗