dyn7 - M which can rotate about the xed point O, as shown...

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2.032 DYNAMICS Fall 2004 Problem Set No. 7 Out : Wednesday, November 3, 2004 Due : Wednesday, November 10, 2004 at the beginning of class Problem 1 The force F acts horizontally at the end of the four-member linkage shown below. The linkage is described by the generalized coordinates ξ 1 = θ 1 , ξ 2 = θ 2 , ξ 3 = θ 3 , ξ 4 = θ 4 . Find the generalized forces Ξ 1 , Ξ 2 conjugate to the generalized coordinates ξ 1 , ξ 2 and due to the force F . You may not assume that θ 1 , θ 2 , θ 3 , θ 4 are small angles. 1 Courtesy of Prof. T. Akylas. Used with permission.
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Problem 2 A pendulum consists of a rod of length L , mass m , and centroidal moment of inertia 1 12 mL 2 with a frictionless pivot at one end. The pendulum is suspended from a flywheel of radius R and mass
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Unformatted text preview: M which can rotate about the xed point O, as shown below. (a) Select a complete and independent set of generalized coordinates. (Please dene these coordinates clearly .) (b) Derive the Lagrangian equations of motion without making any approximations (small angles, etc.). L g R O 2 Courtesy of Prof. T. Akylas. Used with permission. Problem 3 Consider a bead of mass m sliding without friction on a rotating ring with radius r and negligible mass, as shown in the Fgure. The ring rotates about the vertical axis with constant angular velocity . Derive the equation of motion of the bead using DAlemberts principle. 3...
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dyn7 - M which can rotate about the xed point O, as shown...

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