Pendulum — Small-Angle Approximation
Assumptions
Over what range of initial angles does the small-angle pendulum approximation remain adequate for these measurements?
An angle-independent period for a simple pendulum of fixed length.
Initial angle: θ / ° · Period: T / s
Reference scale is an assumed response noise floor, not measured uncertainty.
- Simple pendulum: point-like bob and effectively massless rigid suspension.
- Fixed length L = 1 m and approximately constant g = 9.80665 m/s².
- Negligible damping and sufficiently small oscillation angle for the baseline approximation.
Small initial angles; adequacy depends on the measurement scale and coverage.
The small-angle approximation can become increasingly inadequate as oscillation angle grows. Its theoretical period is fixed, never fitted to disguise amplitude dependence. Measurement effects, damping, or geometry could also produce disagreement.
Read the methodology →Model fit
Period (s) vs. initial angle (°)
Period vs. initial angle
T / sMeasurementsFixed theoretical referenceBest hinge comparisonTransition sensitivity range
4 linked measurements selected. Choose one point or row to inspect its exact values.
Residuals
ΔT / sResidual = measured period − reference prediction. A sustained pattern matters more than a single unusual point.