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Topic: [HM] The Foucault pendulum at the CNAM
Replies: 4   Last Post: Jan 28, 1999 2:57 PM

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Michael Deakin

Posts: 64
Registered: 12/3/04
Re: [HM] The Foucault pendulum.
Posted: Jan 27, 1999 12:59 AM
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John Dawson wrote:

> Although that is rather an old-fashioned science museum, it is one of the
> few places I've been that has a Foucault pendulum marked to show where the
> bob will be at a given hour -- the point being that it does *not* go
> through a full circle in 24 hours, as many suppose. (It would only do so at
> the poles.) I confess that I myself was unaware of the latitude dependence
> until I visited the CNAM. The precise equation involved is a simple example
> of a natural context in which the cosecant function arises.

Some years ago, a sequence of Foucault pendulums was built here at
Monash by the late Carl Moppert of this department and (now Emeritus)
Professor Bill Bonwick of Electrical Engeineering. The latest of
this series still functions in the building which houses my office
and it takes up the whole of an otherwise unused liftwell.

Bonwick devised a unique drive that can only accelerate the pendulum
(and by just enough) in the direction of its motion, thius avoiding
the problem of "running down".

A more serious problem with all Foucault pendulums is that of
"ellipsing". For a pendulum to swing in a plane is an unstable mode
of oscillation. The full solution is illustrated on the cover of the
Dover edition of Routh's "Advanced dynamics of Rigid Bodies" and it
consists of an elliptical motion with the ends of the ellipse
rotating at a steady rate. This "ellipsing" must be suppressed as it
is a much larger effect than the Foucault effect, which is hard to
deteect if ellipsing is taking place.

Most Foucault pendulums use a device known as a Charron ring to this
end, but the theory of this is not entirely agreed and the results
not wonderfully good. In the American Journal of Physics of (some
10?) years ago there is a lengthy discussion on the matter.

Moppert & Bonwick did not use a Charron ring, but opted for a sponge
rubber sleeve at the maximum amplitude of the swing. Later this was
replaced by further electrical controls.

The results are still in considerable error, but are the best ever
achieved. Moppert conducted an extensive correspondence with the
curators of all known Foucault pendulums at the time and many
curators quite openly admitted to "cheating", by advancing or
retarding the pendulum in the hours that the public had no access.

A smaller version of the Moppert-Bonwick pendulum hangs in the McCoy
(Geology) Building at the University of Melbourne. Monash has
another Foucault Pendulum on display in its Physics department, but
this is a smaller and conventional affair with a Charron ring.

For more on the theory, see Moppert's article in Q J R Ast Soc 21
(1980), pp 108-118.

Mike Deakin

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