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Mechanical Vibration Teaser Problem
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- Subject: Mechanical Vibration Teaser Problem
- From: Eddie Gonzalez <Eagonzal(--nospam--at)ENG.CI.LA.CA.US>
- Date: Thu, 21 Jan 1999 16:18:14 -0800
One of our interns had the following mechanical vibration problem to solve. I thought maybe some of you on the server would get a kick in trying to solve it -- take you back to your college years. Its a text book problem (Single Degree of Freedom System) so keep it simple. A uniform bar with mass "m" lies symmetrically across two rapidly rotating, fixed rollers, A and B, with distance L=2.0 cm between the bar's center of mass and each roller. The rollers, whose direction of rotation are shown in the figure, slip against the bar with coefficient of kinetic friction uk = 0.40. Suppose the bar is diplaced horizontally by a distance X, and then released. Q: What is the angular frequency w of the resulting horizontal simple harmonic (back and forth) motion of the bar? |<------L------>|<-------L------->| ==============M============== O O (clockwise (counter-clockwise rotation) rotation) assume: Prior to displacement, bar is stable, with the force of one roller couteracting the force of the other. Hints: D' Alambert's Principle, Sum of F = ma Enjoy, ed gonzalez
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