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This paper addresses mechanical oscillation problems employing a proposed modified variant of coyote optimizer. Coyote optimization algorithm (COA) is a new meta-heuristic which mimics the social behavior of coyotes. COA suffers with stagnation problems and immature convergence while solving optimization problems. In this paper, the COA is hybridized with Laplace Crossover operator and new culture tendency strategies are adapted, modified variants of coyote optimization algorithm (MvCOA). The proposed MvCOA is presented to approximately solve mechanical oscillation problems independently of their order, form, and stated conditions. With the fundamental concepts of ordinary differential equations and Fourier series expansion, mechanical oscillation problems can be modeled as a problem of optimization whereby the optimization task is achieved using the proposed MvCOA. Five different ordinary differential equations and four mechanical oscillation problems are solved approximately and then compared with their corresponding exact solutions. The statistical analysis validates that the presented MvCOA is an effective algorithm for different optimization problems. However, from the empirical results, it is visible that the suggested MvCOA approximate approach was able to reach a successful performance solving different mechanical oscillation problems.<\/jats:p>","DOI":"10.1177\/00375497221101058","type":"journal-article","created":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T02:19:18Z","timestamp":1654654758000},"page":"1161-1178","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["A modified variant of coyote optimization algorithm for solving ordinary differential equations and oscillatory mechanical problems"],"prefix":"10.1177","volume":"98","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5810-7423","authenticated-orcid":false,"given":"Heba F","family":"Eid","sequence":"first","affiliation":[{"name":"Faculty of Science, Al-Azhar University, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Romany F","family":"Mansour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, New Valley University, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik","family":"Cuevas","sequence":"additional","affiliation":[{"name":"Department of Electronics, University of Guadalajara, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2022,6,7]]},"reference":[{"key":"bibr1-00375497221101058","volume-title":"Mechanical vibration","author":"Krodkiewski JM.","year":"2008"},{"key":"bibr2-00375497221101058","first-page":"41","volume":"172","author":"Collins J","year":"2019","journal-title":"Bridge Eng"},{"key":"bibr3-00375497221101058","volume-title":"Elementary differential equations and boundary value problems","author":"Boyce WE","year":"1997","edition":"6"},{"key":"bibr4-00375497221101058","first-page":"779","volume":"179","author":"Lee ZY.","year":"2006","journal-title":"Appl Math Comput"},{"key":"bibr5-00375497221101058","doi-asserted-by":"publisher","DOI":"10.12988\/ijcms.2006.06068"},{"key":"bibr6-00375497221101058","first-page":"657","volume":"188","author":"Darania P","year":"2007","journal-title":"Appl Math Comput"},{"key":"bibr7-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.03.045"},{"key":"bibr8-00375497221101058","first-page":"291","volume":"112","author":"Yal\u00e7\u0131nba\u015f S","year":"2000","journal-title":"Appl Math Comput"},{"key":"bibr9-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1007\/BF01182160"},{"key":"bibr10-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1007\/s00231-008-0446-9"},{"key":"bibr11-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1515\/IJNSNS.2006.7.4.411"},{"key":"bibr12-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.09.070"},{"key":"bibr13-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1016\/j.applthermaleng.2008.01.012"},{"key":"bibr14-00375497221101058","volume-title":"Differential transform and its applications for electrical circuits","author":"Zhou JK.","year":"1986"},{"key":"bibr15-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2007.09.025"},{"key":"bibr16-00375497221101058","first-page":"150","volume":"5","author":"Torabi M","year":"2012","journal-title":"Recent Pat Mech Eng"},{"key":"bibr17-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2011.09.049"},{"key":"bibr18-00375497221101058","doi-asserted-by":"publisher","DOI":"10.1016\/j.apt.2011.02.013"},{"key":"bibr19-00375497221101058","first-page":"39","volume-title":"Proceedings of the sixth international symposium on micro machine and human science","author":"Eberhart R"},{"key":"bibr20-00375497221101058","volume-title":"Ant colony optimization","author":"Dorigo M","year":"2010"},{"key":"bibr21-00375497221101058","unstructured":"Pham D, Ghanbarzadeh A, Koc E, et al. 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