Underdamped oscillations of a mass between two springs
The oscillations of one mass m suspended between two different springs, assuming a friction force proportional to the velocity ( x ˙ ) , have been studied. For this purpose, an assembly for this system has been made. The movement of the mass is recorded with a smartphone and analysed with Tracker. I...
- Autores:
-
Herrera-Suárez H.J.
Morales-Aranguren H.L.
Muñoz J.H.
Ossa-Novoa J.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2022
- Institución:
- Universidad de Ibagué
- Repositorio:
- Repositorio Universidad de Ibagué
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unibague.edu.co:20.500.12313/3831
- Acceso en línea:
- https://hdl.handle.net/20.500.12313/3831
- Palabra clave:
- Friction
Newton’s laws
Nonlinear oscillations
Underdamped oscillator motion
- Rights
- openAccess
- License
- http://purl.org/coar/access_right/c_abf2
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Underdamped oscillations of a mass between two springs |
| title |
Underdamped oscillations of a mass between two springs |
| spellingShingle |
Underdamped oscillations of a mass between two springs Friction Newton’s laws Nonlinear oscillations Underdamped oscillator motion |
| title_short |
Underdamped oscillations of a mass between two springs |
| title_full |
Underdamped oscillations of a mass between two springs |
| title_fullStr |
Underdamped oscillations of a mass between two springs |
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Underdamped oscillations of a mass between two springs |
| title_sort |
Underdamped oscillations of a mass between two springs |
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Herrera-Suárez H.J. Morales-Aranguren H.L. Muñoz J.H. Ossa-Novoa J. |
| dc.contributor.author.none.fl_str_mv |
Herrera-Suárez H.J. Morales-Aranguren H.L. Muñoz J.H. Ossa-Novoa J. |
| dc.subject.proposal.eng.fl_str_mv |
Friction Newton’s laws Nonlinear oscillations Underdamped oscillator motion |
| topic |
Friction Newton’s laws Nonlinear oscillations Underdamped oscillator motion |
| description |
The oscillations of one mass m suspended between two different springs, assuming a friction force proportional to the velocity ( x ˙ ) , have been studied. For this purpose, an assembly for this system has been made. The movement of the mass is recorded with a smartphone and analysed with Tracker. It is obtained that the graph of the position of the mass m in function of the time is similar to that of an underdamped harmonic oscillator. The registered data with Tracker are exported to Excel and fit to a nonlinear model through the expression x ( t ) = A e − λ t sin ( ω t + α ) . The nonlinear equation of motion is numerically solved with the free Octave package. This solution es very sensitive to the mass of the particle and the stretching of the springs |
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2022 |
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2022-08-23 |
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2023-10-17T20:08:16Z |
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2023-10-17T20:08:16Z |
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Artículo de revista |
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Herrera-Suárez, H. J., Morales-Aranguren, H. L., Muñoz, J., & Ossa-Novoa, J. (2022). Underdamped oscillations of a mass between two springs. Physics Education, 57(6), 065010. https://doi.org/10.1088/1361-6552/ac8409 |
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00319120 |
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https://hdl.handle.net/20.500.12313/3831 |
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Herrera-Suárez, H. J., Morales-Aranguren, H. L., Muñoz, J., & Ossa-Novoa, J. (2022). Underdamped oscillations of a mass between two springs. Physics Education, 57(6), 065010. https://doi.org/10.1088/1361-6552/ac8409 00319120 |
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https://hdl.handle.net/20.500.12313/3831 |
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eng |
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eng |
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065010 |
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57 |
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Physics Education |
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Goldstein, H, Poole, C P, Safko, J L (2013) Classical Mechanics 3rd edn Harlow Pearson New International Edition De Lange, O L, Pierrus, J (2010) Solved Problems in Classical Mechanics: Analytical and Numerical Solutions With Comments. 1st edn New York Oxford University Press Alonso, M, Finn, E J (1986) FÍsica, I. MecÁnica Wilmington, NC Addison Wesley Iberoamericana Chaudhuri, R N (2001) Waves and Oscillations 2nd edn New Delhi New Age Int. Thornton, S T, Marion, J B (2006) Classical Dynamics of Particles and Systems. 5th edn Mexico Thomson Brooks/cole Serway, R A, Jewett, J W (2018) Physics for Scientists and Engineers 10th edn Mexico Cengage Learning Amezquita, A., Delgado, M., Rasero, D. Intrinsically non-linear oscillating systems (2021) Revista Brasileira de Ensino de Fisica, 43, pp. 1-7. http://www.scielo.br/scielo.php?script=sci_serial&pid=1806-1117&lng=en&nrm=iso doi: 10.1590/1806-9126-RBEF-2021-0110 Schott, D. Modelling of oscillators: General framework and simulation projects (2010) Global Journal of Engineering Education, 12 (1), pp. 17-23. http://www.wiete.com.au/journals/GJEE/Publish/vol12no1/06-Schott.pdf Younes, Y.K., Fawzy, A., Ibrahim, I.M., El-Butch, A.M.A. An investigation of friction dynamics of mass spring system with base excitation (2005) American Society of Mechanical Engineers, Tribology Division, TRIB, (16), pp. 127-133. ISBN: 0791842339; 978-079184233-1 doi: 10.1115/IMECE2005-80275 Mohazzabi, P. Theory and examples of intrinsically nonlinear oscillators (2004) American Journal of Physics, 72 (4), pp. 492-498. doi: 10.1119/1.1624114 Detcheva, V., Spassov, V. A simple nonlinear oscillator: Analytical and numerical solution (1993) Physics Education, 28 (1), art. no. 007, pp. 39-42.doi: 10.1088/0031-9120/28/1/007 Thomchick, J., McKelvey, J.P. Anharmonic vibrations of an “Ideal” hooke's law oscillator (1978) American Journal of Physics, 46 (1), pp. 40-45. doi: 10.1119/1.11180 TU Graz Graz University of Technology 2022 A mass on a frictionless table connected to two springs (available at http://lampx.tugraz.at/hadley/physikm/script/oscillations/2springs.en.php García, F A (2016) Oscilador no lineal (available at www.sc.ehu.es/sbweb/fisica3/oscilaciones/dosMuelles/dosMuelles.html (2020) (available at http://physlets.org/tracker GNU Octave 2022 (available at www.gnu.org/software/octave/index Analytical Balance Precisa ES 120A with self calibration system, scales and measuring instruments (available at https://scales-measuring.com/en/analytical-balances/2060-analytical-balance-precisa-es-120a.html |
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Herrera-Suárez H.J.0bd3e1a1-fb38-4e11-b546-edb3cf2a3666-1Morales-Aranguren H.L.5036f1db-d2ab-4983-a3a6-afca676de1b7-1Muñoz J.H.8ac4592b-a2c7-4338-bc5c-a89efd80ea16-1Ossa-Novoa J.08c2e3be-ef79-4163-a6fb-761b0963699b-12023-10-17T20:08:16Z2023-10-17T20:08:16Z2022-08-23The oscillations of one mass m suspended between two different springs, assuming a friction force proportional to the velocity ( x ˙ ) , have been studied. For this purpose, an assembly for this system has been made. The movement of the mass is recorded with a smartphone and analysed with Tracker. It is obtained that the graph of the position of the mass m in function of the time is similar to that of an underdamped harmonic oscillator. The registered data with Tracker are exported to Excel and fit to a nonlinear model through the expression x ( t ) = A e − λ t sin ( ω t + α ) . The nonlinear equation of motion is numerically solved with the free Octave package. This solution es very sensitive to the mass of the particle and the stretching of the springsapplication/pdfHerrera-Suárez, H. J., Morales-Aranguren, H. L., Muñoz, J., & Ossa-Novoa, J. (2022). Underdamped oscillations of a mass between two springs. Physics Education, 57(6), 065010. https://doi.org/10.1088/1361-6552/ac840900319120https://hdl.handle.net/20.500.12313/3831engReino Unido06501057Physics EducationGoldstein, H, Poole, C P, Safko, J L (2013) Classical Mechanics 3rd edn Harlow Pearson New International EditionDe Lange, O L, Pierrus, J (2010) Solved Problems in Classical Mechanics: Analytical and Numerical Solutions With Comments. 1st edn New York Oxford University PressAlonso, M, Finn, E J (1986) FÍsica, I. MecÁnica Wilmington, NC Addison Wesley IberoamericanaChaudhuri, R N (2001) Waves and Oscillations 2nd edn New Delhi New Age Int.Thornton, S T, Marion, J B (2006) Classical Dynamics of Particles and Systems. 5th edn Mexico Thomson Brooks/coleSerway, R A, Jewett, J W (2018) Physics for Scientists and Engineers 10th edn Mexico Cengage LearningAmezquita, A., Delgado, M., Rasero, D. Intrinsically non-linear oscillating systems (2021) Revista Brasileira de Ensino de Fisica, 43, pp. 1-7. http://www.scielo.br/scielo.php?script=sci_serial&pid=1806-1117&lng=en&nrm=iso doi: 10.1590/1806-9126-RBEF-2021-0110Schott, D. Modelling of oscillators: General framework and simulation projects (2010) Global Journal of Engineering Education, 12 (1), pp. 17-23. http://www.wiete.com.au/journals/GJEE/Publish/vol12no1/06-Schott.pdfYounes, Y.K., Fawzy, A., Ibrahim, I.M., El-Butch, A.M.A. An investigation of friction dynamics of mass spring system with base excitation (2005) American Society of Mechanical Engineers, Tribology Division, TRIB, (16), pp. 127-133. ISBN: 0791842339; 978-079184233-1 doi: 10.1115/IMECE2005-80275Mohazzabi, P. Theory and examples of intrinsically nonlinear oscillators (2004) American Journal of Physics, 72 (4), pp. 492-498. doi: 10.1119/1.1624114Detcheva, V., Spassov, V. A simple nonlinear oscillator: Analytical and numerical solution (1993) Physics Education, 28 (1), art. no. 007, pp. 39-42.doi: 10.1088/0031-9120/28/1/007Thomchick, J., McKelvey, J.P. Anharmonic vibrations of an “Ideal” hooke's law oscillator (1978) American Journal of Physics, 46 (1), pp. 40-45. doi: 10.1119/1.11180TU Graz Graz University of Technology 2022 A mass on a frictionless table connected to two springs (available at http://lampx.tugraz.at/hadley/physikm/script/oscillations/2springs.en.phpGarcía, F A (2016) Oscilador no lineal (available at www.sc.ehu.es/sbweb/fisica3/oscilaciones/dosMuelles/dosMuelles.html(2020) (available at http://physlets.org/trackerGNU Octave 2022 (available at www.gnu.org/software/octave/indexAnalytical Balance Precisa ES 120A with self calibration system, scales and measuring instruments (available at https://scales-measuring.com/en/analytical-balances/2060-analytical-balance-precisa-es-120a.htmlSubject to subscriber status, reasonable amounts of IOP copyright-protected material (other than logos) may be reproduced, distributed or communicated to others free of charge in any format or media for the purposes of research for a non-commercial purpose, or for private study, or for internal circulation within an organisation. This is subject to the material being reproduced accurately and not being used in a misleading context.info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)https://creativecommons.org/licenses/by-nc-nd/4.0/https://iopscience.iop.org/article/10.1088/1361-6552/ac8409FrictionNewton’s lawsNonlinear oscillationsUnderdamped oscillator motionUnderdamped oscillations of a mass between two springsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionPublicationTEXTScopus - Document details - Underdamped oscillations of a mass between two springs.pdf.txtScopus - Document details - Underdamped oscillations of a mass between two springs.pdf.txtExtracted texttext/plain2655https://repositorio.unibague.edu.co/bitstreams/80e5221c-ef2f-4379-9961-e62432806b73/download8bb41b2577b773db47812218073db2b7MD53THUMBNAILScopus - Document details - Underdamped oscillations of a mass between two springs.pdf.jpgScopus - Document details - Underdamped oscillations of a mass between two springs.pdf.jpgGenerated Thumbnailimage/jpeg7932https://repositorio.unibague.edu.co/bitstreams/7bd5f4e2-bc43-4fb0-88fd-4b05a8dd4140/download11e7a24a9478082bcb0e675b2cdf9529MD54LICENSElicense.txtlicense.txttext/plain; charset=utf-8134https://repositorio.unibague.edu.co/bitstreams/9da6a613-3f56-409a-83b9-269bb98b4426/download2fa3e590786b9c0f3ceba1b9656b7ac3MD52ORIGINALScopus - Document details - Underdamped oscillations of a mass between two springs.pdfScopus - Document details - Underdamped oscillations of a mass between two springs.pdfapplication/pdf159528https://repositorio.unibague.edu.co/bitstreams/43c6bbbe-03bf-4458-b192-fa95bf796fbe/download45ce48341a242a962021e8fa36e8dc32MD5120.500.12313/3831oai:repositorio.unibague.edu.co:20.500.12313/38312023-10-18 03:00:48.139https://creativecommons.org/licenses/by-nc-nd/4.0/Subject to subscriber status, reasonable amounts of IOP copyright-protected material (other than logos) may be reproduced, distributed or communicated to others free of charge in any format or media for the purposes of research for a non-commercial purpose, or for private study, or for internal circulation within an organisation. 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