Comparative analysis of linear and non-linear free vibrations of harmonic oscillator
Free vibrations of a harmonic oscillator in the form of a mathematical pendulum in linear and nonlinear formulations are considered. Their comparative analysis is carried out as a conservative system with one degree of freedom. To solve a nonlinear differential equation, the finite difference method...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2021-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/57/e3sconf_catpid2021_01028.pdf |
| _version_ | 1818438228414300160 |
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| author | Kulterbaev Khusen Vodakhova Valentina Baragunova Lyalusya Dadova Marina Shogenova Mariana |
| author_facet | Kulterbaev Khusen Vodakhova Valentina Baragunova Lyalusya Dadova Marina Shogenova Mariana |
| author_sort | Kulterbaev Khusen |
| collection | DOAJ |
| description | Free vibrations of a harmonic oscillator in the form of a mathematical pendulum in linear and nonlinear formulations are considered. Their comparative analysis is carried out as a conservative system with one degree of freedom. To solve a nonlinear differential equation, the finite difference method and Euler’s scheme are used. Specific examples are given, the limits of the mathematical pendulum deviations angles, at which the solutions of linear and nonlinear problems practically coincide, are determined. The law of potential and kinetic energy sum conservation is used for the oscillations of conservative systems. The conclusions are drawn for the practical application of the results obtained. |
| first_indexed | 2024-12-14T17:37:14Z |
| format | Article |
| id | doaj.art-c43d848005944f9090dde661c3a38dec |
| institution | Directory Open Access Journal |
| issn | 2267-1242 |
| language | English |
| last_indexed | 2024-12-14T17:37:14Z |
| publishDate | 2021-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | E3S Web of Conferences |
| spelling | doaj.art-c43d848005944f9090dde661c3a38dec2022-12-21T22:52:57ZengEDP SciencesE3S Web of Conferences2267-12422021-01-012810102810.1051/e3sconf/202128101028e3sconf_catpid2021_01028Comparative analysis of linear and non-linear free vibrations of harmonic oscillatorKulterbaev Khusen0Vodakhova Valentina1Baragunova Lyalusya2Dadova Marina3Shogenova Mariana4North Caucasus Federal UniversityKabardino-Balkarian State University named after H.M. BerbekovKabardino-Balkarian State University named after H.M. BerbekovKabardino-Balkarian State University named after H.M. BerbekovKabardino-Balkarian State University named after H.M. BerbekovFree vibrations of a harmonic oscillator in the form of a mathematical pendulum in linear and nonlinear formulations are considered. Their comparative analysis is carried out as a conservative system with one degree of freedom. To solve a nonlinear differential equation, the finite difference method and Euler’s scheme are used. Specific examples are given, the limits of the mathematical pendulum deviations angles, at which the solutions of linear and nonlinear problems practically coincide, are determined. The law of potential and kinetic energy sum conservation is used for the oscillations of conservative systems. The conclusions are drawn for the practical application of the results obtained.https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/57/e3sconf_catpid2021_01028.pdf |
| spellingShingle | Kulterbaev Khusen Vodakhova Valentina Baragunova Lyalusya Dadova Marina Shogenova Mariana Comparative analysis of linear and non-linear free vibrations of harmonic oscillator E3S Web of Conferences |
| title | Comparative analysis of linear and non-linear free vibrations of harmonic oscillator |
| title_full | Comparative analysis of linear and non-linear free vibrations of harmonic oscillator |
| title_fullStr | Comparative analysis of linear and non-linear free vibrations of harmonic oscillator |
| title_full_unstemmed | Comparative analysis of linear and non-linear free vibrations of harmonic oscillator |
| title_short | Comparative analysis of linear and non-linear free vibrations of harmonic oscillator |
| title_sort | comparative analysis of linear and non linear free vibrations of harmonic oscillator |
| url | https://www.e3s-conferences.org/articles/e3sconf/pdf/2021/57/e3sconf_catpid2021_01028.pdf |
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