{"id":4674,"date":"2019-01-14T02:12:39","date_gmt":"2019-01-14T07:12:39","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/?page_id=4674"},"modified":"2019-01-15T18:29:30","modified_gmt":"2019-01-15T23:29:30","slug":"linearization-of-eoms-2","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/animations\/linearization-of-eoms-2\/","title":{"rendered":"Linearization of EOMs"},"content":{"rendered":"

<\/p>\n

Linearization of EOM’s: Influence of equilibrium state on response<\/span><\/h2>\n
\n

Consider the single-DOF problem of a thin bar pinned to ground with a constant horizontal force F acting at the free end of the bar.<\/span><\/p>\n

\"\"<\/p>\n

Using Lagrange’s equations, the nonlinear EOM for this system is:<\/span><\/p>\n

\"\"<\/p>\n

This EOM, linearized about the equilibrium state of:<\/span><\/p>\n

\"\"<\/p>\n

becomes:<\/span><\/p>\n

\"\"<\/p>\n

where<\/span><\/p>\n

\"\"<\/p>\n

This says that for a small perturbation about the equilibrium state, the response of the bar will oscillate about with this equilibrium state.<\/span><\/p><\/blockquote>\n

Shown below are animations of the free response of the bar for two values of F\/mg. From these animations, can you see the influence of the force F on the equilibrium state and the frequency of oscillations about this equilibrium??<\/span><\/p>\n

<\/p>\n

<\/p>\n

\n

\u00a0<\/span><\/p>\n

\n","protected":false},"excerpt":{"rendered":"

Linearization of EOM’s: Influence of equilibrium state on response Consider the single-DOF problem of a thin bar pinned to ground with a constant horizontal force F acting at the free end of the bar. Using Lagrange’s equations, the nonlinear EOM for this system is: This EOM, linearized about the equilibrium state of: becomes: where This … Continue reading Linearization of EOMs<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-4674","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4674","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/comments?post=4674"}],"version-history":[{"count":5,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4674\/revisions"}],"predecessor-version":[{"id":5027,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4674\/revisions\/5027"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/14"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/media?parent=4674"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}