A Forgotten Simple Pendulum Period Equation

The variation of the period of oscillation of a pendulum with the amplitude is known as “circular error” to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude,...

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Bibliographic Details
Published in:The Physics teacher 2021-11, Vol.59 (8), p.646-647
Main Author: Hinrichsen, Peter F.
Format: Article
Language:English
Subjects:
Accuracy
Laboratory Equipment
Mathematical Formulas
Motion
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Summary:The variation of the period of oscillation of a pendulum with the amplitude is known as “circular error” to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude, but the simple equation due to Denman, TD(φ0)=T0/(1−φ02/16),(1) which is more accurate than many in the literature, seems to have been forgotten.
ISSN:0031-921X
1943-4928
DOI:10.1119/10.0006917