Hi Randall,


Consider a circular magnet hanging from a horizontal iron bar:


(see: http://jjlahr.com/science/psn/pivots )


If the center of mass of the magnet is at its center, then there will be
no

preferred position which could be considered an infinite period in terms
of

a pendulum.


Next consider the situation with the center of mass on the edge of the


magnet.


(see: http://jjlahr.com/science/psn/pivots )


The center of mass will rise a bit with rotation of the magnet, but not
as much

as would a simple pendulum with length equal to the diameter of the
magnet.

Thus the period is longer than the "equivalent"
pendulum.


If a rod were connected to this magnet with a weight on it's end, then
the

period will always be a bit longer than would be expected from the

pendulum with the length of the rod, but the longer the rod the less the


difference would be.


If the magnet were stuck to another magnet with the same diameter,

then the center of rotation would always be the center of the upper
magnet.


If the lower pivot of a Lehman were designed to give the equivalent
of

a very long boom, one would still be limited in the period if the
upper

pivot remained a single point.  If both pivots worked with large
round

surfaces running on parallel planar surfaces, then long periods could
be

achieved without having to make the axis between the upper and=20
lower

pivots so nearly vertical.


I'm not really suggesting this as a viable mechanical arrangement, 

but just as food for thought.


Cheers,

John





At 01:36 PM 11/23/2002, you wrote:

Hi
All,

 

In pondering this issue, it would seem to me
that as 2 convex surfaces roll, the contact point would move in the same
direction as the mass.  This would put the pivot off center and
effectively shorten the boom.  Depending on the radii involved the
geometry with respect to the upper pivot will also be affected.  The
effects would be magnified on a small instrument because the boom angles
of motion for the same displacement will be larger.  In addition the
small instrument is operating at a much finer angle between the upper and
lower pivots so again the effect will be more pronounced.  Possibly
the ball is more stable because the period is in effect lessening with
displacement from center.  Any thoughts or calculations to either
support or shoot me down?  I am using an archery point against an
aircraft bolt head.  My FFT always has a peak between 18 and 25
seconds with very little adjustment needed.  I did go completely off
the side when the river flooded 2 miles east of here and had to reset
then and again when the water dropped.