Pendulum motion on modified trajectories The cycloidal pendulum as an old-time GPS.
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| Title: | Pendulum motion on modified trajectories The cycloidal pendulum as an old-time GPS. |
|---|---|
| Authors: | Beszeda, Imre1 beszedaimre@gmail.com, Stonawski, Tamás1 stonawski@gmail.com |
| Source: | Latin-American Journal of Physics Education. Dec2021, Vol. 15 Issue 4, p1-7. 7p. |
| Subject Terms: | *Physics textbooks, *Teaching, Classical mechanics, Pendulums, Harmonic oscillators |
| Abstract (English): | According to physics textbooks, measurements show that the period of a simple gravity pendulum does not change significantly at small displacement angles (up to about 5°), but increases at larger displacements. For small swings, i.e. for angles less than 5°, the constant period is explained by the fact that in this case the curvature of the pendulum's trajectory is negligible, the pendulum approximates a simple harmonic oscillator (where the oscillation time is independent of the amplitude). This 5° limit is not really based on the results obtained from measurements, but rather on a differential equation (which could be difficult to explain in primary and secondary school in the absence of mathematical background), where the small angle approximation sin α≈α can be applied below 5°, and so we get a much more simple equation. We wanted to check where this limit might be in the measurements and whether this amplitude dependence could actually be measured below this value. [ABSTRACT FROM AUTHOR] |
| Abstract (Spanish): | Según los libros de texto de física, las mediciones muestran que el período de un péndulo de gravedad simple no cambia significativamente en ángulos de desplazamiento pequeños (hasta unos 5°), pero aumenta en desplazamientos más grandes. Para oscilaciones pequeñas, es decir, para ángulos inferiores a 5°, el período constante se explica por el hecho de que en este caso la curvatura de la trayectoria del péndulo es despreciable, el péndulo se aproxima a un oscilador armónico simple (donde el tiempo de oscilación es independiente de la amplitud). Este límite de 5° no se basa realmente en los resultados obtenidos de las mediciones, sino más bien en una ecuación diferencial (que podría ser difícil de explicar en la escuela primaria y secundaria en ausencia de antecedentes matemáticos), donde la aproximación del ángulo pequeño sen α≈α se puede aplicar por debajo de 5°, y así obtenemos una ecuación mucho más simple. Queríamos verificar dónde podría estar este límite en las mediciones y si esta dependencia de amplitud realmente podría medirse por debajo de este valor. [ABSTRACT FROM AUTHOR] |
| Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 155595528 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Pendulum motion on modified trajectories The cycloidal pendulum as an old-time GPS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Beszeda%2C+Imre%22">Beszeda, Imre</searchLink><relatesTo>1</relatesTo><i> beszedaimre@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Stonawski%2C+Tamás%22">Stonawski, Tamás</searchLink><relatesTo>1</relatesTo><i> stonawski@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Latin-American+Journal+of+Physics+Education%22">Latin-American Journal of Physics Education</searchLink>. Dec2021, Vol. 15 Issue 4, p1-7. 7p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Physics+textbooks%22">Physics textbooks</searchLink><br />*<searchLink fieldCode="DE" term="%22Teaching%22">Teaching</searchLink><br /><searchLink fieldCode="DE" term="%22Classical+mechanics%22">Classical mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Pendulums%22">Pendulums</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: According to physics textbooks, measurements show that the period of a simple gravity pendulum does not change significantly at small displacement angles (up to about 5°), but increases at larger displacements. For small swings, i.e. for angles less than 5°, the constant period is explained by the fact that in this case the curvature of the pendulum's trajectory is negligible, the pendulum approximates a simple harmonic oscillator (where the oscillation time is independent of the amplitude). This 5° limit is not really based on the results obtained from measurements, but rather on a differential equation (which could be difficult to explain in primary and secondary school in the absence of mathematical background), where the small angle approximation sin α≈α can be applied below 5°, and so we get a much more simple equation. We wanted to check where this limit might be in the measurements and whether this amplitude dependence could actually be measured below this value. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Spanish) Group: Ab Data: Según los libros de texto de física, las mediciones muestran que el período de un péndulo de gravedad simple no cambia significativamente en ángulos de desplazamiento pequeños (hasta unos 5°), pero aumenta en desplazamientos más grandes. Para oscilaciones pequeñas, es decir, para ángulos inferiores a 5°, el período constante se explica por el hecho de que en este caso la curvatura de la trayectoria del péndulo es despreciable, el péndulo se aproxima a un oscilador armónico simple (donde el tiempo de oscilación es independiente de la amplitud). Este límite de 5° no se basa realmente en los resultados obtenidos de las mediciones, sino más bien en una ecuación diferencial (que podría ser difícil de explicar en la escuela primaria y secundaria en ausencia de antecedentes matemáticos), donde la aproximación del ángulo pequeño sen α≈α se puede aplicar por debajo de 5°, y así obtenemos una ecuación mucho más simple. Queríamos verificar dónde podría estar este límite en las mediciones y si esta dependencia de amplitud realmente podría medirse por debajo de este valor. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 1 Subjects: – SubjectFull: Physics textbooks Type: general – SubjectFull: Teaching Type: general – SubjectFull: Classical mechanics Type: general – SubjectFull: Pendulums Type: general – SubjectFull: Harmonic oscillators Type: general Titles: – TitleFull: Pendulum motion on modified trajectories The cycloidal pendulum as an old-time GPS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Beszeda, Imre – PersonEntity: Name: NameFull: Stonawski, Tamás IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 18709095 Numbering: – Type: volume Value: 15 – Type: issue Value: 4 Titles: – TitleFull: Latin-American Journal of Physics Education Type: main |
| ResultId | 1 |
