Fourier analysis of nonlinear pendulum oscillations
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , |
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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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 |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100405 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172018000100405 |
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) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
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 |
_version_ |
1752122423312908288 |