A simple pendulum’s small-angle period depends on its length and local gravity.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §16.4 (Paul Peter Urone and Roger Hinrichs)OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
A simple pendulum’s small-angle period depends on its length and local gravity. The small-angle approximation replaces sin θ by θ in radians.
| Symbol | Meaning | Units |
|---|---|---|
| Period | ||
| Pivot-to-bob-center pendulum length | ||
| Acceleration Due to Gravity |
Estimate the small-angle swing period.
Compare periods for different pendulum lengths.
Find the small-angle period of a pendulum of length 1 m where g = 9.80 m/s².
OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
Assumptions
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