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Re: Mechanical Vibration Teaser Problem

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Mechanical Vibration Teaser Problem
• From: Jim Kestner <jkestner(--nospam--at)somervilleinc.com>
• Date: Fri, 22 Jan 1999 07:48:32 -0600

```Believe it or not, I had this same problem 30 years ago on a test in my Vibration
course! The professors must be recycling problems.

Jim Kestner, P.E.
Green Bay, Wi.

Eddie Gonzalez wrote:

> 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
>
>

```