{"id":13738,"date":"2022-04-22T09:59:48","date_gmt":"2022-04-22T13:59:48","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=13738"},"modified":"2024-10-10T09:36:13","modified_gmt":"2024-10-10T13:36:13","slug":"homework-h6-j-2","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/chapter-6-discussions\/homework-h6-j-2\/","title":{"rendered":"Homework H6.C.17"},"content":{"rendered":"

\"\"<\/p>\n

Discussion and hints:
\n<\/strong><\/em>The derivation of the dynamical equation of motion (EOM) for a system is a straight-forward application of what we have learned from Chapter 5 in using the Newton-Euler equations. The goal in deriving the EOM is to end up with a single differential equation in terms of a single dependent variable that describes the motion of the system. Here in this problem, we want our EOM to be in terms of x<\/em>(t).<\/p>\n

Recall the following f<\/em>our-step plan<\/em><\/span> outline in the lecture book and discussed in lecture:<\/p>\n

Step 1: FBDs
\n<\/strong><\/em>Draw individual FBDs of the disk and the block. Define a rotational coordinate \u03b8<\/em>\u00a0for the disk.<\/p>\n

Step 2: Kinetics (Newton\/Euler)
\n<\/strong><\/em>Write down the Newton\/Euler equations for the disk and the block.<\/p>\n

Step 3: Kinematics<\/strong><\/em>
\nUse the no-slip condition at at both the top and bottom locations on the disk to relate x<\/em> and \u03b8<\/em>.<\/p>\n

Step 4: EOM<\/strong><\/em>
\nCombine your Newton\/Euler equations and your kinematics equations to arrive at the single differential equation of motion for the system.<\/p>\n

For this problem, you need to determine the particular solution for the EOM corresponding to the excitation.<\/p>\n

\n

Any questions?<\/p>\n","protected":false},"excerpt":{"rendered":"

Discussion and hints: The derivation of the dynamical equation of motion (EOM) for a system is a straight-forward application of what we have learned from Chapter 5 in using the Newton-Euler equations. The goal in deriving the EOM is to end up with a single differential equation in terms of a single dependent variable that … Continue reading Homework H6.C.17<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":15017,"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-13738","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/13738","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/page"}],"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=13738"}],"version-history":[{"count":3,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/13738\/revisions"}],"predecessor-version":[{"id":15198,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/13738\/revisions\/15198"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/15017"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=13738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}