Coupled oscillations of the Wilberforce pendulum unveiled by smartphones
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.
2022 | |
Coupled oscillators Measuring instruments, Gyroscope Spring constants Rotational dynamics Programming languages Wilberforce pendulum Coordinate system Educational practices Physics education research |
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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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collection | COLIBRI |
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 |
format | article |
id | COLIBRI_92b3a423c76a26d8d337f360f2b6f19d |
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 |
language | eng |
language_invalid_str_mv | en |
network_acronym_str | COLIBRI |
network_name_str | COLIBRI |
oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/41673 |
publishDate | 2022 |
reponame_str | COLIBRI |
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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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 |