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# Mechanical Vibration Teaser Problem

• To: seaint(--nospam--at)seaint.org
• 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

```