Coupled oscillations of the Wilberforce pendulum unveiled by smartphones

Gallot, Thomas - Gau de León, Daniel - García-Tejera, Rodrigo

Resumen:

The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but colorful device that features longitudinal and torsional oscillations, catching the eye of students and teachers, and offering a fantastic environment to study coupled oscillations at qualitative and quantitative levels. However, the experimental setups that are commonly used to simultaneously acquire both oscillation types can be cumbersome and/or costly, often requiring two synchronised cameras, or motion sensors and photo-gates integrated by an expensive analog-to-digital converter. Here, we show that a smartphone can be the perfect device for recording the oscillations of a Wilberforce pendulum composed of just an educational helical spring and a can. Our setup employs a smartphone’s accelerator and gyroscope to acquire data from the longitudinal and torsional oscillations, respectively. This setup can successfully record both normal modes and beats. Furthermore, we show that our experimentally obtained time-series and power spectra are in great agreement with simulations of the motion equations. In addition, we critically analyse how to set the initial conditions to observe both normal modes and beats. We believe our study contributes to bring the striking physics of the Wilberforce pendulum closer to undergraduate classrooms with low-cost, highly-accessible materials.


Detalles Bibliográficos
2022
Coupled oscillators
Measuring instruments,
Gyroscope
Spring constants
Rotational dynamics
Programming languages
Wilberforce pendulum
Coordinate system
Educational practices
Physics education research
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/41673
Acceso abierto
Licencia Creative Commons Atribución (CC - By 4.0)
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author Gallot, Thomas
author2 Gau de León, Daniel
García-Tejera, Rodrigo
author2_role author
author
author_facet Gallot, Thomas
Gau de León, Daniel
García-Tejera, Rodrigo
author_role author
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dc.contributor.filiacion.none.fl_str_mv Gallot Thomas, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.
Gau de León Daniel, Universidad de la República (Uruguay). Facultad de Ingeniería.
García-Tejera Rodrigo
dc.creator.none.fl_str_mv Gallot, Thomas
Gau de León, Daniel
García-Tejera, Rodrigo
dc.date.accessioned.none.fl_str_mv 2023-12-04T20:02:54Z
dc.date.available.none.fl_str_mv 2023-12-04T20:02:54Z
dc.date.issued.none.fl_str_mv 2022
dc.description.abstract.none.fl_txt_mv The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but colorful device that features longitudinal and torsional oscillations, catching the eye of students and teachers, and offering a fantastic environment to study coupled oscillations at qualitative and quantitative levels. However, the experimental setups that are commonly used to simultaneously acquire both oscillation types can be cumbersome and/or costly, often requiring two synchronised cameras, or motion sensors and photo-gates integrated by an expensive analog-to-digital converter. Here, we show that a smartphone can be the perfect device for recording the oscillations of a Wilberforce pendulum composed of just an educational helical spring and a can. Our setup employs a smartphone’s accelerator and gyroscope to acquire data from the longitudinal and torsional oscillations, respectively. This setup can successfully record both normal modes and beats. Furthermore, we show that our experimentally obtained time-series and power spectra are in great agreement with simulations of the motion equations. In addition, we critically analyse how to set the initial conditions to observe both normal modes and beats. We believe our study contributes to bring the striking physics of the Wilberforce pendulum closer to undergraduate classrooms with low-cost, highly-accessible materials.
dc.description.es.fl_txt_mv Publicado en: American Journal of Physics, 2023, 91(11): 873-878. DOI: doi.org/10.1119/5.0138680
dc.format.extent.es.fl_str_mv 21 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Gallot, T, Gau de León, D y García-Tejera, R. "Coupled oscillations of the Wilberforce pendulum unveiled by smartphones". [Preprint]. arXiv:2212.06949 [physics.ed-ph] https://doi.org/10.48550/arXiv.2212.06949
dc.identifier.doi.none.fl_str_mv 10.48550/arXiv.2212.06949
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/41673
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv arXiv
dc.relation.ispartof.es.fl_str_mv arXiv:2212.06949, dic 2022, pp 1-20
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.subject.es.fl_str_mv Coupled oscillators
Measuring instruments,
Gyroscope
Spring constants
Rotational dynamics
Programming languages
Wilberforce pendulum
Coordinate system
Educational practices
Physics education research
dc.title.none.fl_str_mv Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
dc.type.es.fl_str_mv Artículo
dc.type.none.fl_str_mv info:eu-repo/semantics/article
dc.type.version.none.fl_str_mv info:eu-repo/semantics/publishedVersion
description Publicado en: American Journal of Physics, 2023, 91(11): 873-878. DOI: doi.org/10.1119/5.0138680
eu_rights_str_mv openAccess
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identifier_str_mv Gallot, T, Gau de León, D y García-Tejera, R. "Coupled oscillations of the Wilberforce pendulum unveiled by smartphones". [Preprint]. arXiv:2212.06949 [physics.ed-ph] https://doi.org/10.48550/arXiv.2212.06949
10.48550/arXiv.2212.06949
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
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publishDate 2022
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repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución (CC - By 4.0)
spelling Gallot Thomas, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.Gau de León Daniel, Universidad de la República (Uruguay). Facultad de Ingeniería.García-Tejera Rodrigo2023-12-04T20:02:54Z2023-12-04T20:02:54Z2022Gallot, T, Gau de León, D y García-Tejera, R. "Coupled oscillations of the Wilberforce pendulum unveiled by smartphones". [Preprint]. arXiv:2212.06949 [physics.ed-ph] https://doi.org/10.48550/arXiv.2212.06949https://hdl.handle.net/20.500.12008/4167310.48550/arXiv.2212.06949Publicado en: American Journal of Physics, 2023, 91(11): 873-878. DOI: doi.org/10.1119/5.0138680The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but colorful device that features longitudinal and torsional oscillations, catching the eye of students and teachers, and offering a fantastic environment to study coupled oscillations at qualitative and quantitative levels. However, the experimental setups that are commonly used to simultaneously acquire both oscillation types can be cumbersome and/or costly, often requiring two synchronised cameras, or motion sensors and photo-gates integrated by an expensive analog-to-digital converter. Here, we show that a smartphone can be the perfect device for recording the oscillations of a Wilberforce pendulum composed of just an educational helical spring and a can. Our setup employs a smartphone’s accelerator and gyroscope to acquire data from the longitudinal and torsional oscillations, respectively. This setup can successfully record both normal modes and beats. Furthermore, we show that our experimentally obtained time-series and power spectra are in great agreement with simulations of the motion equations. In addition, we critically analyse how to set the initial conditions to observe both normal modes and beats. We believe our study contributes to bring the striking physics of the Wilberforce pendulum closer to undergraduate classrooms with low-cost, highly-accessible materials.Submitted by Festari Camila (camifestari@gmail.com) on 2023-12-02T04:24:22Z No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 2212.06949.pdf: 468676 bytes, checksum: e1bef06270e5f62dee58bf9318ab32a7 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-12-04T18:53:02Z (GMT) No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 2212.06949.pdf: 468676 bytes, checksum: e1bef06270e5f62dee58bf9318ab32a7 (MD5)Made available in DSpace by Seroubian Mabel (mabel.seroubian@seciu.edu.uy) on 2023-12-04T20:02:54Z (GMT). No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 2212.06949.pdf: 468676 bytes, checksum: e1bef06270e5f62dee58bf9318ab32a7 (MD5) Previous issue date: 202221 h.application/pdfenengarXivarXiv:2212.06949, dic 2022, pp 1-20Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)Coupled oscillatorsMeasuring instruments,GyroscopeSpring constantsRotational dynamicsProgramming languagesWilberforce pendulumCoordinate systemEducational practicesPhysics education researchCoupled oscillations of the Wilberforce pendulum unveiled by smartphonesArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaGallot, ThomasGau de León, DanielGarcía-Tejera, RodrigoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/41673/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/41673/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse
spellingShingle Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
Gallot, Thomas
Coupled oscillators
Measuring instruments,
Gyroscope
Spring constants
Rotational dynamics
Programming languages
Wilberforce pendulum
Coordinate system
Educational practices
Physics education research
status_str publishedVersion
title Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
title_full Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
title_fullStr Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
title_full_unstemmed Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
title_short Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
title_sort Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
topic Coupled oscillators
Measuring instruments,
Gyroscope
Spring constants
Rotational dynamics
Programming languages
Wilberforce pendulum
Coordinate system
Educational practices
Physics education research
url https://hdl.handle.net/20.500.12008/41673