set_cv3_problem - Problem Set CV3 MMAE 501 Engineering...

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Problem Set CV3 MMAE: 501 Engineering Analysis I Kevin W. Cassel Mechanical, Materials and Aerospace Engineering Department Illinois Institute of Technology 10 West 32nd Street Chicago, IL 60616 [email protected] Problem Reference Problem # 1: Hildebrand, Chapter 2, Problem 57 Problem # 2: Hildebrand, Chapter 2, Problem 60 Problem # 3: Hildebrand, Chapter 2, Problem 71 Problem # 4: Hildebrand, Chapter 2, Problem 78 Problem # 5: Hildebrand, Chapter 2, Problem 87 Problem # 6: Hildebrand, Chapter 2, Problem 89(a) c 2007 Kevin W. Cassel 1
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Problem # 1 A particle of mass m is moving vertically, under the action of gravity and a resistive force numerically equal to k times the downward displacement x from an equilibrium position. Show that the equation of Hamilton’s principle is of the form δ Z t 2 t 1 1 2 m ˙ x 2 + mgx - 1 2 kx 2 dt = 0 , and obtain the Euler equation. Problem # 2 Three masses are connected in series to a fixed support, by linear springs. Figure 1.
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