Fourier analysis of nonlinear pendulum oscillations

Detalhes bibliográficos
Autor(a) principal: Singh,Inderpreet
Data de Publicação: 2018
Outros Autores: Arun,Palakkandy, Lima,Fabio
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100405
Resumo: Since the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 9 0 ∘. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.
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spelling Fourier analysis of nonlinear pendulum oscillationsSimple pendulumNonlinear oscillationsFourier seriesSince the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 9 0 ∘. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.Sociedade Brasileira de Física2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100405Revista Brasileira de Ensino de Física v.40 n.1 2018reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2017-0151info:eu-repo/semantics/openAccessSingh,InderpreetArun,PalakkandyLima,Fabioeng2019-05-24T00:00:00Zoai:scielo:S1806-11172018000100405Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2019-05-24T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Fourier analysis of nonlinear pendulum oscillations
title Fourier analysis of nonlinear pendulum oscillations
spellingShingle Fourier analysis of nonlinear pendulum oscillations
Singh,Inderpreet
Simple pendulum
Nonlinear oscillations
Fourier series
title_short Fourier analysis of nonlinear pendulum oscillations
title_full Fourier analysis of nonlinear pendulum oscillations
title_fullStr Fourier analysis of nonlinear pendulum oscillations
title_full_unstemmed Fourier analysis of nonlinear pendulum oscillations
title_sort Fourier analysis of nonlinear pendulum oscillations
author Singh,Inderpreet
author_facet Singh,Inderpreet
Arun,Palakkandy
Lima,Fabio
author_role author
author2 Arun,Palakkandy
Lima,Fabio
author2_role author
author
dc.contributor.author.fl_str_mv Singh,Inderpreet
Arun,Palakkandy
Lima,Fabio
dc.subject.por.fl_str_mv Simple pendulum
Nonlinear oscillations
Fourier series
topic Simple pendulum
Nonlinear oscillations
Fourier series
description Since the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 9 0 ∘. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100405
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2017-0151
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.40 n.1 2018
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
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reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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