## Foucault Pendulum

This project is suggested by Professor Cary Forest and is to hang a Foucault Pendulum in what was once an elevator shaft in the atrium of Chamberlin Hall (see photos). The pendulum requires a drive system to maintain constant amplitude and a method of recording the trajectory on the floor. For those unfamiliar with the Foucault pendulum, imagine a long simple pendulum at the north pole, the mass free to move over the surface of a sphere of radius equal to the pendulum length. The plane of a planar oscillation remains fixed in space in an (approximate) inertial frame moving with the Earth around the Sun. The Earth rotates relative to such an inertial frame so, relative to an Earth observer, the plane of oscillation appears to rotate (precess) by 360 degrees per sidereal day (23.93 hours) or about 15 degrees/hr, and can thereby demonstrating the rotation of the Earth. A pendulum at the equator undergoing a N-S or E-W oscillation will not appear to precess. The precession rate relative to the Earth is proportional to the sin of the latitude angle and is about 10 degree/hour at 43.0667 degrees N. The precession is ascribable to the Coriolis (pseudo)force acting along with the harmonic restoring force in the noninertial frame attached to the Earth. An elliptical (nonplanar) motion may precess due to anharmonicity in the restoring force. The precession rate is proportional to the elliptical area. This effect or asymmetry in the pendulum support forces can mimic or mask the precession.

This project may be the focus of a Kinect controlled music project of Prof. Steve Dembski (Music).

Participants: Prof. Cary Forest, Prof. Carlsmith, Prof. Steven Dembski, Peter Weix (Plasma physics), Joseph Sterle (Undergraduate Research Scholar 2013)

### Resources

History of Sterling Hall Foucault pendulum (15 m length, 0.5 m amplitude) https://wiki.physics.wisc.edu/facultywiki/FoucaultPendulum, https://mywebspace.wisc.edu/pjweix/web/History.html?uniq=-bsn31u, https://mywebspace.wisc.edu/pjweix/web/RichardsLetter1.pdf?uniq=-bs3hnz,

Wikipedia description and list of pendulum installations http://en.wikipedia.org/wiki/Foucault_pendulum, http://en.wikipedia.org/wiki/List_of_Foucault_pendulums#United_States

Youtube video of the pendum at the Museum of Science and Industry in Chicago https://www.youtube.com/watch?v=iqpV1236_Q0

Oregon Convention Center. (Don't stand under that thing!) https://www.youtube.com/watch?v=6oYvffE6iGY.

American Journal of Physics (all Foucault pendulum articles) http://scitation.aip.org.ezproxy.library.wisc.edu/search?value1=foucault+pendulum&option1=all&option12=resultCategory&value12=ResearchPublicationContent

A simple solution to the mechanics and the analogy to the neutral kaon system: The precession of a Foucault pendulum viewed as a beat phenomenon of a conical pendulum subject to a Coriolis force, Geoffrey I. Opat, Am. J. Phys. 59 , 822 (1991) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.16729 , Classical illustrations of CP violation in kaon decays, Jonathan L. Rosner and Scott A. Slezak, Am. J. Phys. 69 , 44 (2001) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.1289212

Description of supports, safe catcher, energizer, and "Crane ring." Foucault pendulum ‘‘wall clock’’,H. Richard Crane, Am. J. Phys. 63, 33 (1995); http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.17765

Sustained Foucault Pendulums, R. Stuart Mackay Am. J. Phys. 21 , 180 (1953) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.1933395

A Direct Treatment of the Foucault Pendulum William J. Noble Am. J. Phys. 20 , 334 (1952) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.1933230

Short Foucault pendulum: A way to eliminate the precession due to ellipticity H. Richard Crane Am. J. Phys. 49 , 1004 (1981) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.12655

15 m minimum length? One needs a way to interest a viewer over a time scale of a minute. The Foucault pendulum as a murder weapon and a physicist’s delight, H. Richard Crane, Phys. Teach. 28 , 264 (1990) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.2343022

Graphics tablet to digitize pendulum tip, Hands‐On Earth Rotation, Manfred Euler and Gert Braune, Phys. Teach. 40 , 432 (2002) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.1517888

Foucault pendulum with eddy‐current damping of the elliptical motion G. Mastner , V. Vokurka , M. Maschek , E. Vogt and H. P. Kaufmann Rev. Sci. Instrum. 55 , 1533 (1984) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1063/1.1137615

Failed attempt to power https://neil.fraser.name/news/2011/01/07/

A simplified discussion of the mechanics and use of a Crane ring and magnetic force to reduce anharmonic restoring forces http://www.physics.uoguelph.ca/foucault/foucault1.html

Interpretation in terms of geometrical transport and connection to Berry's phase Foucault pendulum through basic geometry,Jens von Bergmann and HsingChi von Bergmann, Am. J. Phys. 75 , 888 (2007) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.2757623 , A. Tomita and R. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986). http://dx.doi.org.ezproxy.library.wisc.edu/10.1103/PhysRevLett.57.937

Analysis of asymmetric support , Foucault Pendulum Experiment by Kamerlingh Onnes and Degenerate Perturbation Theory, E. O. Schulz-DuBois Am. J. Phys. 38 , 173 (1970) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.1976270

A 3-m pendulum using heat induced elongation/contraction to maintain oscillation: A sustained demonstration foucault pendulum, Scott McClatchey , Neal Flint and James H. Kraakevik, Phys. Teach. 19 , 134 (1981) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.2340722

A electromagnetic drive circuit: The driving mechanism for a Foucault pendulum (revisited) Joseph Priest and Michael J. Pechan, Am. J. Phys. 76 , 188 (2008) ; http://dx.doi.org.ezproxy.library.wisc.edu/10.1119/1.2800359

Theory F.P. Zhuralev, “A controlled Foucault pendulum as a model of a class of free gyros,” Mechanics of Solids 32(6), 21–28 (1995)

Using a loudspeaker as a piston driven pendulum. http://www.millersville.edu/physics/experiments/034/index.php

The parametrically maintained Foucault pendulum and its perturbations. http://www.jstor.org/stable/pdfplus/2398398.pdf?acceptTC=true&acceptTC=true&jpdConfirm=true

Paper on a parametrically maintained Foucault Pendulum and its perturbations. http://allais.info/priorartdocs/pippard.pdf

Damping http://arxiv.org/html/physics/0210121 , arxiv.org/pdf/physics/0306081‎

Robert Nelson, Marty Olsen paper "The pendulum: Rich physics from a simple system" http://link.aip.org/link/?AJPIAS/54/112/1 describes quadratic damping, bouyancy and extra air mass, effects in support...

### Things to try

A review of conventional explanations of anomalous observations during solar eclipses H. R. Salva, “Searching the Allais effect during the total sun eclipse of 11 July 2010,” Phys. Rev. D 83, 067302 (2011). 3C. P. Duif, preprint arXiv:gr-qc/0408023v5 (2004). 4X. E. Amador, J. Phys.: Conf. Ser. 24, 247 (2005).

### Progress

Status 23 Sep '13 Undergraduate Research Scholar and first year student Joseph Sterle will work on the Foucault pendulum project for 2 credits in Fall 2013 under Carlsmith's supervision under the auspices of Garage Physics.

Joseph will design and test the excitation mechanism for the Foucault pendulum in the atrium of Chamberlin Hall. In particular, he will study parametric excitation via lifting the support point as an alternate/supplement to magnetic excitation with a ring of magnetics. He will read the appropriate section of Landau and Lifshitz 'Mechanics' on parametric oscillations and the pdf from Princeton students posted at the Garage Physics 'Active mechanical stabilization of structures' suggested project. Joseph will measure the damping time of the actual pendulum in order to design the excitation mechanism and do model calculations of the design parameters needed to prevent the disruption of the Earth rotation signal in the pendulum motion, and to damp elliptical motion if necessary, and to ensure the drive (phased to support the intended slow rotation) does not force an unnatural motion. Joseph will attend 3rd Thursday garage meetings, create a poster about his project, and write a final 10-page paper.

30 Oct '13 Roof support installed.

17 Dec '13 Beginning tests

None: Foucault Pendulum (last edited 2014-04-11 16:33:19 by DuncanCarlsmith)