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Homework4_2010 - ME 562 Advanced Dynamics Summer 2010...

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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 0 l and the particle has a velocity 0 v in the direction shown. In the motion that follows, the spring stretches to a maximum length of 0 4 /3 l . Assuming no gravity (motion in horizontal plane), find the spring stiffness k as a function of m , 0 l , and 0 v . (Problem 3-15 in the text).
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  • Fall '10
  • Particle, smooth horizontal table, differential equation models, appropriate initial conditions, energy conservation principle

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