{"id":23693,"date":"2026-04-23T12:01:57","date_gmt":"2026-04-23T16:01:57","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=23693"},"modified":"2026-04-27T13:45:43","modified_gmt":"2026-04-27T17:45:43","slug":"homework-h6-i-sp26","status":"publish","type":"post","link":"https:\/\/www.purdue.edu\/freeform\/me274\/2026\/04\/23\/homework-h6-i-sp26\/","title":{"rendered":"Homework H6.I &#8211; Sp26"},"content":{"rendered":"<table style=\"width: 100%;border-collapse: collapse;background-color: #faf7f7\">\n<tbody>\n<tr>\n<td style=\"width: 100%\"><a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2023\/11\/bDnvYr-collection_fspI-dragged-26.pdf\"><span style=\"font-size: 12pt\"><em><strong>Problem statement<\/strong><\/em><\/span><\/a><br \/>\n<a href=\"https:\/\/youtu.be\/FKGPH_FdtDw\"><span style=\"font-size: 12pt\"><em><strong>Solution video<\/strong><\/em><\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<p><em><strong><span style=\"font-size: 14pt\">DISCUSSION THREAD<\/span><\/strong><\/em><\/p>\n<div data-post-id=\"12645\" class=\"insert-page insert-page-12645 \"><p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-12646\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/11\/Screen-Shot-2021-11-03-at-9.02.45-AM-300x149.jpg\" alt=\"\" width=\"300\" height=\"149\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/11\/Screen-Shot-2021-11-03-at-9.02.45-AM-300x149.jpg 300w, https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/11\/Screen-Shot-2021-11-03-at-9.02.45-AM.jpg 349w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><em><strong>Discussion and hints<\/strong><\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2021\/11\/H6C_01.gif\" width=\"476\" height=\"410\" \/><\/p>\n<p>The above shows the results of simulations on this problem for two frequencies of excitation, \u03c9. The upper plot where \u03c9 is less than the natural frequency, \u03c9<sub>n<\/sub>, and the lower plot where \u03c9 is greater than \u03c9<sub>n<\/sub>. In each plot, the <span style=\"color: #ff0000\"><strong><em>RED<\/em><\/strong><\/span> curve is the forcing F(t) and the <span style=\"color: #0000ff\"><em><strong>BLUE<\/strong><\/em><\/span> curve is the particular solution of the EOM, x<sub>P<\/sub>(t). As can be seen from these simulation results:<\/p>\n<ul>\n<li>The response for <em>\u03c9 &lt; \u03c9<sub>n<\/sub><\/em> has the steady-state response of x<sub>P<\/sub>(t) moving <span style=\"text-decoration: underline\"><em>in phase<\/em><\/span> with the forcing F(t). That is, during the time that the block is displaced to the right, the force is acting to the right. Conversely, during the time that the block is displaced to the left, the force is acting to the left.<\/li>\n<li>The response for <em>\u03c9 &gt; \u03c9<sub>n<\/sub><\/em> has the steady-state response of x<sub>P<\/sub>(t) moving <span style=\"text-decoration: underline\"><em>180\u00b0 out of\u00a0phase<\/em><\/span> with the forcing F(t). That is, during the time that the block is displaced to the right, the force is acting to the left, and during the time that the block is displaced to the left, the force is acting to the right.<\/li>\n<\/ul>\n<p>In your analysis for this problem, you will be determining the natural frequency <em>\u03c9<sub>n\u00a0<\/sub><\/em>of the system, along with the steady-state response. Be sure to check your answer in the end: does it demonstrate the phase relations seen in the above simulation results?<\/p>\n<hr \/>\n<p>Any questions?? Please ask\/answer questions regarding this homework problem through the &#8220;Leave a Comment&#8221; link above.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problem statement Solution video DISCUSSION THREAD<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-23693","post","type-post","status-publish","format-standard","hentry","category-chapter-6-homework"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23693","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/comments?post=23693"}],"version-history":[{"count":3,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23693\/revisions"}],"predecessor-version":[{"id":24974,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/posts\/23693\/revisions\/24974"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=23693"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/categories?post=23693"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/tags?post=23693"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}