{"id":4694,"date":"2019-01-14T02:32:54","date_gmt":"2019-01-14T07:32:54","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/?page_id=4694"},"modified":"2019-01-14T07:40:44","modified_gmt":"2019-01-14T12:40:44","slug":"two-dof-string-model","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/chapter-ii-animations\/two-dof-string-model\/","title":{"rendered":"Two-DOF string model"},"content":{"rendered":"

\u00a0As we have seen from this lecture, the qualitative nature of the free response of a system will depend on the particular initial conditions given to the system. For example, for a two-DOF system released from<\/i> rest<\/i> (a zero initial velocity for all points in the system):<\/p>\n

 <\/p>\n\n\n\n\n\n
FIRST MODE<\/span><\/i><\/b><\/center>
\u00a0<\/center><\/td>\n
If the initial conditions are in the <\/span>first<\/span><\/i> mode<\/span><\/p>\n

<\/p><\/blockquote>\n

the then response will be <\/span>HARMONIC<\/span> having a frequency of the <\/span>first natural frequency<\/span><\/i> and the shape of the <\/span>response will remain in the first mode<\/span><\/i>.<\/span><\/td>\n<\/tr>\n

SECOND MODE<\/span><\/i><\/b><\/center>
\u00a0<\/center><\/td>\n
If the initial conditions are in the <\/span>second<\/span><\/i> mode<\/span><\/p>\n

<\/p><\/blockquote>\n

then the response will be <\/span>HARMONIC<\/span> having a frequency of the <\/span>second natural frequency<\/span><\/i> and the shape of the <\/span>response will remain in the second mode<\/span><\/i><\/td>\n<\/tr>\n

NON-MODAL RESPONSE<\/span><\/i><\/b><\/center><\/td>\n
For ANY initial conditions other than those in a) and b), the response will be (generally) <\/span>NON-HARMONIC<\/span> and will be a <\/span>LINEAR COMBINATION<\/span> of the two modes.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n
<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

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

\u00a0As we have seen from this lecture, the qualitative nature of the free response of a system will depend on the particular initial conditions given to the system. For example, for a two-DOF system released from rest (a zero initial velocity for all points in the system):   FIRST MODE\u00a0 If the initial conditions are … Continue reading Two-DOF string model<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":4682,"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-4694","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4694","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=4694"}],"version-history":[{"count":9,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4694\/revisions"}],"predecessor-version":[{"id":4740,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4694\/revisions\/4740"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4682"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/media?parent=4694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}