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### t3_04

Course: EM 406, Fall 2009
School: Rose-Hulman
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Word Count: 224

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___________________________ EM406 Name Examination III November 5, 2004 Problem 1 2 4 Total Score /30 /30 /40 /100 Show all work for credit AND Stay in your seat until the end of class AND Turn in your signed help sheet Name EM406 Examination III Problem 1 30 pts November 5, 2004 A mass is suspended below a uniform slender bar as shown. Using Lagrange's equations determine the equations of motion for the...

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___________________________ EM406 Name Examination III November 5, 2004 Problem 1 2 4 Total Score /30 /30 /40 /100 Show all work for credit AND Stay in your seat until the end of class AND Turn in your signed help sheet Name EM406 Examination III Problem 1 30 pts November 5, 2004 A mass is suspended below a uniform slender bar as shown. Using Lagrange's equations determine the equations of motion for the two masses. Assume small angles. m1, L, IG b a k1 O c m2 k2 F1(t) F2(t) Name EM406 Examination III Problem 2 30 pts November 5, 2004 If in the previous problem you assume the damping is zero, F1 = 0, and you substitute in numbers for known parameters you find the equations of motion are: 10 0 && 2k 1 + 700 - 700 0 = 0 2 && + - 700 x 700 5 sin t x Determine the value of k1 such that the steady-state motion of mass, m2, is zero. Name EM406 Examination III Problem 3 40 pts November 5, 2004 A 3-DOF system governed by coordinates, x1, x2 and x3 is found to have the eigenvalues and modal matrix (I've rounded horribly to save time writing assume these are correct.) 2 1 = 1.86 = 6.00 2 2 2 3 = 9.14 0.48 - 0.26 0.13 [] = 0.96 0 - 0.21 0.68 0.18 0.20 Assume the mass matrix is [M]...

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