ME 562 Advanced Dynamics Summer 2010 HOMEWORK # 4 Due: June 28, 2010 Q1. A massless disc of radius R has an embedded particle of mass m at a distance R/2 from the center. The disc is released from rest in the position shown and rolls without slipping down the fixed inclined plane. Find: (a) the equation of motion of the particle in terms of the angle and its time derivatives; (b) as a function of . This is really integration of the equation of motion starting with the initial condition given above in the statement. Hint: It is easier to do in terms of the energy conservation principle for the particle. (Problem 3-10 in the text). Q2. Initially the spring has its unstretched length 0l and the particle has a velocity 0v in the direction shown. In the motion that follows, the spring stretches to a maximum length of 04 /3 l . Assuming no gravity (motion in horizontal plane), find the spring stiffness k as a function of m , 0l , and 0v . (Problem 3-15 in the text). Q3.
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