{"id":4768,"date":"2019-01-14T12:05:26","date_gmt":"2019-01-14T17:05:26","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/?page_id=4768"},"modified":"2019-01-14T12:16:42","modified_gmt":"2019-01-14T17:16:42","slug":"free-response-of-a-string","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/chapter-iii-animations\/free-response-of-a-string\/","title":{"rendered":"Free response of a string"},"content":{"rendered":"

<\/p>\n

Response of string to initial deformation<\/b><\/span><\/em><\/p>\n

\n\n\n\n
In this example we considered the free response of a fixed-fixed string to a set of initial conditions that resulted from pulling the string at its midpoint and releasing it from rest.<\/p>\n

<\/p>\n

We found that the response is a linear combination of the mode shapes (modal functions) as:<\/p>\n

<\/p>\n

where the response coefficients go as:<\/p>\n

<\/p>\n

That is, the contribution of the higher modes to the overall response drops at a rate of the square of the mode number.<\/p>\n

When twenty modes are included in the above summation, the response of the string is as shown in the response animation to the right (the Matlab code presented in the lecture notes was used to create this animation). Is this what you expected the response to look like?<\/p>\n

 <\/td>\n

\"\"<\/center><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Response of string to initial deformation In this example we considered the free response of a fixed-fixed string to a set of initial conditions that resulted from pulling the string at its midpoint and releasing it from rest. We found that the response is a linear combination of the mode shapes (modal functions) as: where … Continue reading Free response of a string<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":4780,"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-4768","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4768","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=4768"}],"version-history":[{"count":5,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4768\/revisions"}],"predecessor-version":[{"id":4779,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4768\/revisions\/4779"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4780"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/media?parent=4768"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}