ME 274 Spring 2012 Final Examination PROBLEM NO 2 Given Name A homogeneous disk of mass m and radius R rolls without slip on a moving block of mass 2m The center of the disk is connected to ground by a spring of stiffness 2k and the block is connected to ground by a spring of stiffness 3k Point O designates the center of mass of the disk and point C designates the point of contact between the disk and block The motion of the block is prescribed such that x B t bsin t The springs are unstretched when x0 x B 0 Find For this problem a Derive the differential equation of motion EOM for the system in terms of only the coordinate xO and the defined parameters of the problem b Determine the natural frequency of the system n c Derive the expressions for the coefficients of the particular solution of your EOM associated with xO t d What is the amplitude of response when n B xB t
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