MEM423Su07-08_HW1_soln_stud

# MEM423Su07-08_HW1_soln_stud - MEM 423 mechanics of...

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MEM 423: mechanics of Vibrations Home work #1 (due 07/01/08) from text, Edition IV Problem: 2.62 . And (i) In case c, discuss the response of the system if a ϖ m < l p where p and m are the natural frequencies of a ‘traditional’ pendulum and a spring-mass system respectively. (ii) Let g denote the numerical values of the acceleration due to gravity. Then, with the numerical values , plot the response θ (t) for all the three cases {a,b,c}, when the ‘pendulum’ is released from an initial angular displacement of 15 o with zero velocity. In addition, in the case of (c) plot the response when the initial velocity equals “- 15*sqrt(0.5) rad/sec.” and the initial angular displacement equal 15 degrees. Relevance to a-k criteria: a, e

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solution 2.62: (with positive direction of angular motion as shown in text take moments about pivot) (a) k = 0; (b) (c) Since the problem states “is made to vibrate,” we assume that the configuration is so that the system does “vibrate,” allowing the
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MEM423Su07-08_HW1_soln_stud - MEM 423 mechanics of...

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