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RE: Mechanical Vibration Teaser Problem
[Subject Prev][Subject Next][Thread Prev][Thread Next]- To: "'seaint(--nospam--at)seaint.org'" <seaint(--nospam--at)seaint.org>
- Subject: RE: Mechanical Vibration Teaser Problem
- From: "Smith, Steven A" <Steve.Smith(--nospam--at)PSS.Boeing.com>
- Date: Fri, 22 Jan 1999 09:36:16 -0800
For a 1 DOF system, w = sqrt(u*g/L) where for u = 0.4, g = 980 cm/sec^2, L = 2 cm, w = sqrt(0.4 * 980 / 2) = 14 rad /sec. Steve Smith Systems Stress (425) 294-7681 M/S 02-56 > ---------- > From: Eddie Gonzalez[SMTP:Eagonzal(--nospam--at)ENG.CI.LA.CA.US] > Reply To: seaint(--nospam--at)seaint.org > Sent: Thursday, January 21, 1999 4:18 PM > To: seaint(--nospam--at)seaint.org > Subject: Mechanical Vibration Teaser Problem > > 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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