Re: physical pendulums

[Herbert H Gottlieb <herbgottlieb@JUNO.COM>]

On Wed, 22 Sep 1999 23:48:43 -0400 Bob Sciamanda <trebor@VELOCITY.NET>
writes:
> Herb, I think you are confoosed!
>
> The center of oscillation (defined only with respect to a given
> suspension point in the body) is that point which, when used as the
point of
> suspension, gives the same period of small amplitude oscillations.
> That is  not the question asked.

Am I really confoosed ????

According to University Physics, 5th edition by Semat, Zemansky, and
Young
(P205), "It is always possible to find an equivalent simple pendulum
whose
period is equal to that of a physical pedulum." ...... "Thus, so far as
its period
of vibration is concerned, the mass of a physical pendulum may be
considered
to be concentrated at a point whose distance from the pivot is  L=I/mh.
This point is called the CENTER OF OSCILLATION of the pendulum.

Herb
> ----- Original Message -----
> From: Herbert H Gottlieb <herbgottlieb@JUNO.COM>
> To: <PHYS-L@lists.nau.edu>
> Sent: Wednesday, September 22, 1999 11:15 PM
> Subject: Re: physical pendulums
>
>
> > On Wed, 22 Sep 1999 19:30:53 -0700 fred brace <fredb@TELEPORT.COM>
> > writes:
> > > I am using a set of physical science lab materials on the
> pendulum.  One of  the activities asks the students to get a washer, a
bolt
> and a long  wooden  dowel to swing with the same frequency. It says
that if
> the center of  masses line up, then the pendulums will have the same
> frequency.  Is this true?
> >

Herb Replied:

> This is almost true, but not quite true.  For a uniform wooden
> dowel, the center of mass is at  the center of the dowel.
> It's "center of oscillation" is located  at  distance equal
> > to 2/3 of its length , measured from its point of suspension.
> Thus a simple pendulum consisting of a uniform steel washer
> at the end of a string of negligible  mass would have the same
> frequency as the swinging wooden dowel if the  length
> > of the simple pendulum is 2/3 as long as the dowel.  This is
explained in
> detail in most of the popular physics books for introductory physics.
> > Herb Gottlieb from New York City
> > (Where Professor Zemansky of our City College did a great job
> > explaining this in his College and University  Physics testbooks).