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Unformatted text preview: ME 375 Spring 2011 Homework No. 1 Due: Friday, January 21 Problem No. 1 (30%) A system is made up of a homogeneous disk (of mass m and outer radius R) pinned to ground at O. A cable is wrapped around the outer surface of the disk, with one end of the cable attached to a spring of stiffness k and the other end attached to block A (of mass m). The left end of the spring is fixed to ground. A vertical force f t ( ) is applied to block A. The spring is unstretched when = . Assume that the cable does not slip on the disk and that the cable remains taut at all times. Derive the differential equation of motion (EOM) for the system in terms of the output rotation of the disk and the input force f t ( ) . The centroidal mass moment of inertia of a homogeneous disk is given by I O = 1 2 mR 2 . You need to provide complete free body diagrams in the derivation of your EOM. m k m R O A f t ( ) Problem No. 2 (30%) A system is made up of a homogeneous disk (of mass m and outer radius R) pinned to...
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