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me375_fa10_hwk01

# me375_fa10_hwk01 - ME 375 Fall 2010 Homework No 1 Due...

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ME 375 – Fall 2010 Homework No. 1 Due: Friday, September 3 Problem No. 1 (30%) a) Derive the equation of motion (EOM) in terms of the coordinate x for System I shown below. (The springs for this system are unstretched when x = 0 .) b) Derive the EOM in terms of the coordinate x for System II shown below where x represents the displacement of the center O of the wheel. Treat the wheel as a homogeneous disk of mass m and outer radius R . (The springs for this system are unstretched when x = ! = 0 .) Note that neither ! nor its time derivatives should not appear in the final form of your EOM. c) Derive expressions for the undamped natural frequency and the damping ratio for both Systems I and II based on your EOMs in a) and b) above. Compare these results. Which natural frequency is larger? Provide an explanation for your observation. You need to provide complete free body diagrams in the derivation of your EOMs. System I System II k c 2 k x smooth m

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Problem No. 2 (35%) a) Derive the two equations of motion (EOMs) in terms of the coordinates x
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