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# dyn1 - Fall 2004 2.032 DYNAMICS Problem Set No 1 Out...

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2.032 DYNAMICS Fall 2004 Problem Set No. 1 Out : Wednesday, September 15, 2004 Due : Wednesday, September 22, 2004 at the beginning of class Problem 1 (Doctoral Exam, 1999) A pendulum is constructed by attaching a mass m to an extensionless string of fixed length l . The upper end of the string is connected to the uppermost point of a vertical fixed disk of radius R ( R < l/π ), as shown below. At t = 0 the mass hangs at rest at the equilibrium position θ = 0, when it is given an initial velocity v 0 along the horizontal. Derive expressions for the two extreme deflections (in terms of θ ) of the pendulum resulting from this initial perturbation. Do not make a small-angle approximation. g v 0 R m θ 1 Courtesy of Prof. T. Akylas. Used with permission.

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Problem 2 A point mass moves without friction on a horizontal plane. A massless inextensible string is attached to the point mass and led through a hole (see figure below). At time = t 0 the mass moves along a circle with constant velocity v 0 . We gradually pull the free end of the
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