{"id":122633,"date":"2015-09-08T02:00:00","date_gmt":"2015-09-07T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=572ae8c9ec2c2fc2e9ed3369085c0d9e"},"modified":"2015-09-08T02:00:00","modified_gmt":"2015-09-07T23:00:00","slug":"the-duffing-oscillator-with-damping","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=122633","title":{"rendered":"The Duffing oscillator with damping"},"content":{"rendered":"<p>An analytical solution to the differential equation describing the Duffing oscillator with damping<br \/>\nis presented. The damping term of the differential equation and the initial conditions satisfy an<br \/>\nalgebraic equation, and thus the solution is specific for this type of damping. The nonlinear term<br \/>\nof the differential equation is allowed to be considerable compared to the linear term. The solution<br \/>\nis expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic<br \/>\nmodulus. The analytical solution is compared to the numerical solution, and the agreement is found<br \/>\nto be very good. It is established that the period of oscillation is shorter compared to that of a<br \/>\nlinearized model but increasing with time and asymptotically approaching the period of oscillation<br \/>\nof the linear damped model. An explicit expression for the period of oscillation has been derived,<br \/>\nand it is found to be very accurate.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An analytical solution to the differential equation describing the Duffing oscillator with damping<br \/>\nis presented. The damping term of the differential equation and the initial conditions satisfy an<br \/>\nalgebraic equation, and thus the solution is specific&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-122633","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/122633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=122633"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/122633\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=122633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=122633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=122633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}