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Unformatted text preview: ME 240: Introduction to Dynamics and Vibrations Mechanical Engineering Department The University of Michigan Winter 2008 Computer Assignment #1 January 25, 2007 (Due 2/8/2007 Friday) Consider a mass m sliding on a frictionless circular ring subject to a constant thrust force F which is in the tangential direction. The surrounding fluid exerts linear drag force D on the mass which is proportional to the speed of the mass ( | D | = b | v | ). (i) Draw a free-body diagram of m in the position θ shown in Fig.( 1). (ii) Show, using ∑ F = m a , that the equation of motion in the tangential direction is, mR ¨ θ + bR ˙ θ + mg sin θ = F (1) where F = thrust force b = coefficient for drag force D m θ R g Figure 1: A mass m sliding on a circular ring 1 After you obtain the equation of motion Eq.( 1), you can simplify it to ¨ θ + b m ˙ θ + g R sin θ = F mR (2) Hereafter, consider the initial conditions where the particle is at rest at the bottom of the bar . Select the remaining parameters as:...
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This note was uploaded on 03/29/2009 for the course MECHENG 240 taught by Professor Perkins during the Spring '09 term at University of Michigan.
- Spring '09
- Mechanical Engineering