hwk02_soln

hwk02_soln - ME 563 Fall 2011 Homework Prob 2.1 A...

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ME 563 – Fall 2011 Homework Prob. 2.1 A homogeneous wheel having a radius of R and mass of M rolls without slipping on a horizontal surface. A massless, inextensible cable is attached to the center of mass G of the wheel and to a block B (having a mass of m). The cable is pulled over a massless pulley. A spring of stiffness k is attached between G and a fixed wall. The coordinate x describes the position of G, with x being zero when the spring is unstretched. a) Use Lagrange’s equations to develop the EOM for this single-DOF system using the generalized coordinate of x. Assume that the cable remains taut for all motion. b) Using this EOM, determine the value of x corresponding to the equilibrium position of the system. ( Note : The system is in equilibrium when ˙ x = ˙ ˙ x = 0 .) k R massless pulley no slip M m G x B massless, inextensible cable homogeneous wheel g

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ME 563 – Fall 2011 Homework Prob. 2.2 A thin, homogenous bar having a mass of M and length of L is pinned to ground

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hwk02_soln - ME 563 Fall 2011 Homework Prob 2.1 A...

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