{"id":1123,"date":"2023-03-21T09:37:15","date_gmt":"2023-03-21T12:37:15","guid":{"rendered":"https:\/\/revistabrasileiradefisica.com\/rbf\/?p=1123"},"modified":"2023-03-21T09:37:15","modified_gmt":"2023-03-21T12:37:15","slug":"comparison-of-the-analytical-semi-solution-of-the-differential-equation-of-simple-harmonic-motion-with-the-solution-obtained-using-the-runge-kutta-fehlberg-method","status":"publish","type":"post","link":"https:\/\/revistabrasileiradefisica.com\/rbf\/2023\/03\/21\/comparison-of-the-analytical-semi-solution-of-the-differential-equation-of-simple-harmonic-motion-with-the-solution-obtained-using-the-runge-kutta-fehlberg-method\/","title":{"rendered":"Comparison of the Analytical Semi-Solution of the Differential Equation of Simple Harmonic Motion with the Solution obtained using the Runge- Kutta-Fehlberg Method"},"content":{"rendered":"\r\n

Compara\u00e7\u00e3o das Solu\u00e7\u00f5es Semi-Anal\u00edticas e Runge-Kutta-Fehlberg do Modelo de Movimento Harm\u00f4nico Simples<\/em><\/h4>\r\n\r\n\r\n\r\n

DOI<\/strong>: 10.5281\/zenodo.7741020<\/a><\/em><\/p>\r\n\r\n\r\n\r\n

Marco Aur\u00e9lio Amarante Ribeiro<\/strong>
ORCID<\/a> | <\/em> Lattes<\/a> | <\/em> E-mail<\/a><\/em><\/p>\r\n\r\n\r\n\r\n

Jos\u00e9 Helv\u00e9cio Martins<\/strong>
Lattes<\/a> | <\/em> E-mail<\/a><\/em><\/p>\r\n\r\n\r\n\r\n

Abstract: <\/strong>The solution of the differential equation describing simple harmonic motion, represented by a classical pendulum, was discussed. The results of an analytical solution presented in the literature were compared with the results obtained with the Runge-Kutta-Fehlberg method. It was concluded that, practically, there is no difference between the results of these two solutions. A linearized solution has also been considered. This confirms that this solution is valid only for very small amplitudes. Furthermore, the discussions show that the analytical solution presented in the literature cannot be expressed in terms of elementary functions. Therefore, this solution must be considered semi-analytic, as no solution expressed in terms of purely elementary functions has been found in the literature. In this context, it might be interesting to look for such a solution or, perhaps, to demonstrate in detail that this solution can be solved with very good precision using a robust numerical technique.\r\n
Keywords:<\/strong> Simple pendulum, Harmonic motion, Semi-analytical solution, Elliptic integrals, Runge-Kutta-Fehlberg.<\/p>\r\n\r\n\r\n\r\n

Resumo: <\/strong>Foi discutida a solu\u00e7\u00e3o da equa\u00e7\u00e3o diferencial que descreve o movimento harm\u00f4nico simples, representado por um p\u00eandulo cl\u00e1ssico. Os resultados de uma solu\u00e7\u00e3o anal\u00edtica apresentada na literatura foram comparados com os resultados obtidos pelo m\u00e9todo de Runge-Kutta-Fehlberg. Concluiu-se que, praticamente, n\u00e3o h\u00e1 diferen\u00e7as entre os resultados dessas duas solu\u00e7\u00f5es. Uma solu\u00e7\u00e3o linearizada tamb\u00e9m foi considerada. Os resultados confirmaram que esta solu\u00e7\u00e3o \u00e9 v\u00e1lida apenas para amplitudes muito pequenas. Al\u00e9m disso, as discuss\u00f5es mostram que a solu\u00e7\u00e3o apresentada na literatura n\u00e3o pode ser expressa em termos de fun\u00e7\u00f5es elementares, portanto n\u00e3o deve ser considerada completamente anal\u00edtica, mas como uma solu\u00e7\u00e3o semi-anal\u00edtica.<\/em>
\r\nKeywords: <\/strong>P\u00eandulo simples, movimento harm\u00f4nico, solu\u00e7\u00e3o semi-anal\u00edtica, integrais el\u00edpticas, Runge-Kutta-Fehlberg.<\/em><\/p>\r\n\r\n\r\n\r\n

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Compara\u00e7\u00e3o das Solu\u00e7\u00f5es Semi-Anal\u00edticas e Runge-Kutta-Fehlberg do Modelo de Movimento Harm\u00f4nico Simples DOI: 10.5281\/zenodo.7741020 Marco Aur\u00e9lio Amarante RibeiroORCID | Lattes | E-mail Jos\u00e9 Helv\u00e9cio MartinsLattes […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[283],"tags":[307,305,312,314,313,310,309,308,306,304,311],"_links":{"self":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts\/1123"}],"collection":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/comments?post=1123"}],"version-history":[{"count":1,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts\/1123\/revisions"}],"predecessor-version":[{"id":1124,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/posts\/1123\/revisions\/1124"}],"wp:attachment":[{"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/media?parent=1123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/categories?post=1123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/revistabrasileiradefisica.com\/rbf\/wp-json\/wp\/v2\/tags?post=1123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}