A note on the accuracy of a computable approximation for the period of a pendulum

A note on the accuracy of a computable approximation for the period of a pendulum

We discuss the accuracy of a previously proposed computable approximation for the period of the simple pendulum. In particular, we apply known inequalities for the Gaussian hypergeometric function to prove that the associated error is a monotonic function of the maximum angular displacement, α. For...

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Bibliographic Details
Main Authors: Eric Oden, Kendall Richards
Format: Article
Language:English
Published: AIP Publishing LLC 2015-06-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/1.4922268
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spelling doaj-8c7becaafe9b487396f9b81e3b2c0cbc2020-11-24T21:19:20ZengAIP Publishing LLCAIP Advances2158-32262015-06-0156067114067114-410.1063/1.4922268013506ADVA note on the accuracy of a computable approximation for the period of a pendulumEric Oden0Kendall Richards1Department of Mathematics and Computer Science, Southwestern University, Georgetown, Texas 78628, USADepartment of Mathematics and Computer Science, Southwestern University, Georgetown, Texas 78628, USAWe discuss the accuracy of a previously proposed computable approximation for the period of the simple pendulum. In particular, we apply known inequalities for the Gaussian hypergeometric function to prove that the associated error is a monotonic function of the maximum angular displacement, α. For any given range of α, this provides an analytical verification of a precise bound for the associated error.http://dx.doi.org/10.1063/1.4922268
collection DOAJ
language English
format Article
sources DOAJ
author Eric Oden
Kendall Richards
spellingShingle Eric Oden
Kendall Richards
A note on the accuracy of a computable approximation for the period of a pendulum
AIP Advances
author_facet Eric Oden
Kendall Richards
author_sort Eric Oden
title A note on the accuracy of a computable approximation for the period of a pendulum
title_short A note on the accuracy of a computable approximation for the period of a pendulum
title_full A note on the accuracy of a computable approximation for the period of a pendulum
title_fullStr A note on the accuracy of a computable approximation for the period of a pendulum
title_full_unstemmed A note on the accuracy of a computable approximation for the period of a pendulum
title_sort note on the accuracy of a computable approximation for the period of a pendulum
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2015-06-01
description We discuss the accuracy of a previously proposed computable approximation for the period of the simple pendulum. In particular, we apply known inequalities for the Gaussian hypergeometric function to prove that the associated error is a monotonic function of the maximum angular displacement, α. For any given range of α, this provides an analytical verification of a precise bound for the associated error.
url http://dx.doi.org/10.1063/1.4922268
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AT kendallrichards anoteontheaccuracyofacomputableapproximationfortheperiodofapendulum
AT ericoden noteontheaccuracyofacomputableapproximationfortheperiodofapendulum
AT kendallrichards noteontheaccuracyofacomputableapproximationfortheperiodofapendulum
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