Computer Assignment 1 - ME 240 Fall 2011 Computer...

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ME 240 – Fall 2011 Computer Assignment 1 (Due in class October 14, 2011) Consider a mass m , hanging from a massless pendulum rod starting from rest at the position Θ = 0 . The mass moves through a viscous fluid, which generates a damping force proportional to the mass’s velocity and opposing its motion (| D | = c | v | ) . Let R denote the length of the pendulum rod, D denote the drag force imposed onto the mass, T denote the tension force in the pendulum rod, and P denote a tangential control force obeying P = 0.5mgcos(Θ) , and where g is the acceleration due to gravity as shown in the figure. Figure 1: Mass m attached to a pendulum rod of length R 1. Draw a free-body diagram of the mass in the position shown in Figure 1. Clearly show the unit vectors in your free-body diagram and all forces that act on the mass. 2. Using ± ²³ , show that the equation of motion in the tangential direction is ²´ µ¶· ¸ ¹ º»¸ ̇ ¼ ½¾¿²´ µ¶· ¸ ± ²»¸ ̈ 3. After you have obtained this equation of motion, it can be reduced to ¸ ̈ ¼ º ² ¸ ̇ ¹ À¾¿´ » µ¶· ¸ ± ½ P
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4. Assume the values of the constants to be
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This note was uploaded on 10/05/2011 for the course MECHENG 240 taught by Professor Perkins during the Fall '09 term at University of Michigan.

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Computer Assignment 1 - ME 240 Fall 2011 Computer...

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