> > 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.