Simple pendulum period
T = 2π√(L/g) — small-angle isochronism in motion.
Vibration & waves (senior)SHM, resonance, wave formation and interference.
Start here
Simple pendulum period
For small angles, a simple pendulum has T ≈ 2π√(L/g), nearly independent of mass and amplitude.
Small-angle pendulum: period set mainly by length.
Key formulas
T\approx 2\pi\sqrt{L/g}\ddot{\theta}=-\frac{g}{L}\sin\theta
How to use
- Set length L, g, and initial angle θ₀.
- Watch the swing and read the estimated period.
- Compare how T changes with L.
Applications
- Simple pendulum period: Small-angle pendulum: period set mainly by length.
- In class, tune parameters for “Simple pendulum period”, then check against the textbook result.
FAQ
What about large angles?
The small-angle formula underestimates the true period as θ₀ grows.
What does MVP mean on this page?
An interactive sketch with formulas and parameters. Polished Ready labs are the full bench experience.
What does the “Simple pendulum period” lab practice?
Tune parameters and match readouts to the “Simple pendulum period” relations — useful for prep and demos.
How are λ, f, and v related?
v=λf. Speed often set by the medium; frequency by the source.