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Unformatted text preview: ME 375 Homework 2 : Solution September 11, 2009 Problem 1 Derive the equation of motion for the system shown, state any assumptions and draw the free body diagrams. Figure 1: Problem 1 1 Solution: The free body diagram is as follows: Figure 2: Problem 1-FBD Assumptions: • The spring is massless and acts as an ideal spring • The cord only moves vertical • The two disks are both fixed together and only rotate around one point O • Assume no slipping Explanation of symbols used: • x : displacement away from static equilibrium for the mass m • y : displacement away from static equilibrium for the spring • θ : the angular displacement of the disk • F s : force • F k : spring force Important Note: For all the following problem sets, when writing the equations of motion for systems involving the gravitational force, we mea- sure the displacement of the mass from the equilibrium position in order to eliminate the term mg and simplify the mathematical model....
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This note was uploaded on 12/17/2009 for the course IE 383 taught by Professor Leyla,o during the Spring '08 term at Purdue.
- Spring '08