dyn10 - 2.032 DYNAMICS Fall 2004 Problem Set No. 10 Out :...

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Unformatted text preview: 2.032 DYNAMICS Fall 2004 Problem Set No. 10 Out : Wednesday, November 24, 2004 Due : Wednesday, December 1, 2004 at the beginning of class Problem 1 The system below consists of a massless hollow cylindrical tube, joined to a vertical shaft at the point O. The tube is fixed in -direction and = / 4. Inside the tube, moves without friction a mass m which is connected to O through a spring of stiffness k and neutral length of r . Assume that the shaft is rotating with angular velocity about its axis. Using r , as generalized coordinates: (a) Reduce the problem to a one-degree-of-freedom problem for r , that has only potential active forces. (b) Find the equilibria for the reduced system and investigate the stability using Dirichlet theorem. (c) Sketch the trajectories on the ( r , r ) phase plane. Select all parameters to be equal to one, including gravity g. 1 Courtesy of Prof. T. Akylas. Used with permission. Problem 2 (adapted from PhD Qualifying Exam 2003) Reconsider Problem 2 of PS No. 5. Using the same notation,Reconsider Problem 2 of PS No....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.032 taught by Professor Georgehaller during the Fall '04 term at MIT.

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dyn10 - 2.032 DYNAMICS Fall 2004 Problem Set No. 10 Out :...

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