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Rose-Hulman EM 406 - EM 406 Exam 3

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Name ___________________________ EM406 Examination III November 5, 2004 Problem Score 1 /30 2 /30 4 /40 Total /100 Show all work for credit AND Stay in your seat until the end of class AND Turn in your signed help sheetName 30 pts EM406 Examination III Problem 1 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. k2 O a b c m1, L, IG k1 F2(t) m2 F1(t) αName 30 pts EM406 Examination III Problem 2 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: ⎭⎬⎫⎩⎨⎧ω=⎭⎬⎫⎩⎨⎧θ⎥⎦⎤⎢⎣⎡−−++⎭⎬⎫⎩⎨⎧θ⎥⎦⎤⎢⎣⎡tsin50x700700700700k2x200101&&&& Determine the value of k1 such that the steady-state motion of mass, m2, is zero.Name 40 pts EM406 Examination III Problem 3 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.) 14.900.686.1232221=ω=ω=ω []⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡−−=φ20.018.068.021.0096.013.026.048.0 Assume the mass matrix is [M] = 10[I]. Using modal analysis determine the time response of each mass if the system is given the initial conditions 0)0(x)0(x)0(x)0(x3221====&& and 1)0(x1=& and 2)0(x3−= Do not do the algebra associated with the final transformation. Just show me what needs to be


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