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the claim

A pendulum's period is independent of its amplitude

the verdict
REFUTED
the evidence says no
Recorded sources
0 sources for · 4 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Is it true that a pendulum's period is independent of its amplitude?

No. The claim that a pendulum's period is independent of its amplitude is incorrect. In reality, a pendulum's period depends on its amplitude, a dependence that becomes increasingly pronounced at larger angles.

Verdict: REFUTED · 0 sources for, 4 against · Last checked

The analysis

The retrieved literature consistently shows that a pendulum's period varies with its amplitude, particularly outside the small-angle approximation where nonlinear effects require elliptic integrals or specialized approximations. Therefore, the claim is refuted.

Evidence against · 4
An accurate formula for the period of a simple pendulum oscillating beyond the small angle regime
2005
The paper derives formulas demonstrating that a pendulum's period depends on its amplitude outside the small angle regime.
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Lima, F. & Arun, P. (2005). An accurate formula for the period of a simple pendulum oscillating beyond the small angle regime. doi.org. https://doi.org/10.1119/1.2215616

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More against · 3
Review of approximate equations for the pendulum period
2020
The paper reviews approximate equations for measuring the pendulum period as a function of amplitude.
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Hinrichsen, P. (2020). Review of approximate equations for the pendulum period. doi.org. https://doi.org/10.1088/1361-6404/abad10

Fifth-order AGM-formula for the period of a large-angle pendulum
2023
The paper develops formulas for calculating the period of a large-angle pendulum, confirming amplitude dependence.
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Big‐Alabo, A. (2023). Fifth-order AGM-formula for the period of a large-angle pendulum. doi.org. https://doi.org/10.1590/1806-9126-RBEF-2023-0014

Operating Time Modification by Elliptic Integration in Feedforward Control of One-Time Swing-Up Pendulum Using Finite-Time Settling Functions with Half-Odd-Integer Trigonometric Functions
2024
The paper uses elliptic integrals to account for the nonlinearity and period change of a pendulum at different amplitudes.
Get citation
Ohno, M. & Kotake, S. (2024). Operating Time Modification by Elliptic Integration in Feedforward Control of One-Time Swing-Up Pendulum Using Finite-Time Settling Functions with Half-Odd-Integer Trigonometric Functions. doi.org. https://doi.org/10.1109/ONCON62778.2024.10931282

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What does the evidence say?

The retrieved literature consistently shows that a pendulum's period varies with its amplitude, particularly outside the small-angle approximation where nonlinear effects require elliptic integrals or specialized approximations. Therefore, the claim is refuted.

Receipt History
first checked05 Aug 2026
judged → REFUTED · 1205 Aug 2026
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