- Wilberforce pendulum
A Wilberforce pendulum, invented by British physicist
Lionel Robert Wilberforce around 1896 [cite journal|last=Wilberforce|first=Lionel Robert|date=1896|title=On the vibrations of a loaded spiral spring|journal=Philos. Mag.|volume=38|pages=386-392] , consists of amass suspended by a longhelical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanicaloscillator , often used as a demonstration inphysics classes. It can both bob up and down on the spring, and rotate back and forth about it's vertical axis with torsional vibrations. When correctly adjusted and set in motion, it exhibits a curious motion in which periods of purely rotational oscillation gradually alternate with periods of purely up and down oscillation. The energy stored in the device shifts slowly back and forth between the translational 'up and down' oscillation mode and the torsional 'clockwise and counterclockwise' oscillation mode, until the motion gradually dies out. [cite journal
last=Berg
first=Richard E.
coauthors=Marshall, Todd S.
title=Wilberforce pendulum oscillations and normal modes
date=May 4, 1990
journal=American Journal of Physics
volume=59
issue=1
pages=32-37
url=http://faraday.physics.utoronto.ca/PHY182S/WilberforceRefBerg.pdf
accessdate=2008-05-03]Despite the name, it doesn't swing back and forth as ordinary
pendulum s do. The mass usually has opposing pairs of radial 'arms' sticking out horizontally, threaded with small weights that can be screwed in or out to adjust themoment of inertia to 'tune' the torsional vibrationperiod .Explanation
The device's intriguing behavior is caused by a slight coupling between the two motions or
normal mode s, due to the geometry of the spring. When the weight is moving up and down, each downward excursion of the spring causes it to unwind slightly, giving the weight a slight twist. When the weight moves up, it causes the spring to wind slightly tighter, giving the weight a slight twist in the other direction. So when the weight is moving up and down, each oscillation gives a slight back and forth rotational impulse to the weight. In other words, each oscillation some of the energy in the translational mode leaks into the rotational mode. Slowly the up and down movement gets less, and the rotational movement gets greater, until the weight is just rotating and not bobbing.Similarly, when the weight is rotating back and forth, each twist of the weight in the direction that unwinds the spring also reduces the spring tension slightly, causing the weight to sag a little lower. Conversely, each twist of the weight in the direction of winding the spring tighter causes the tension to increase, pulling the weight up slightly. So each oscillation of the weight back and forth causes it to bob up and down more, until all the energy is transferred back from the rotational mode into the translational mode and it is just bobbing up and down, not rotating.
Alternation or 'beat' frequency
The
frequency at which the two modes alternate is equal to the difference between the oscillation frequencies of the modes. The closer in frequency the two motions are, the slower will be the alternation between them. This behavior, common to all coupled oscillators, is analogous to the phenomenon of beats in musical instruments, in which two tones combine to produce a 'beat' tone at the difference between their frequencies. For example, if the pendulum bobs up and down at a rate of fT = 4 Hz, and rotates back and forth at a rate of fR = 4.1 Hz, the alternation rate falt will be:So the motion will change from rotational to translational in 5 seconds and then back to rotational in the next 5 seconds.
The pendulum is usually adjusted by moving the moment of inertia adjustment weights in or out equal amounts on each side, until the rotational frequency is close to the translational frequency, so the alternation period will be slow enough to allow the change between the two modes to be clearly seen.
References
External links
*cite web|last=Pitre|first=John|title=Wilberforce Pendulum|work=Physics 182S lab|publisher=Univ. of Toronto|url=http://faraday.physics.utoronto.ca/PHY182S/WilberforcePendulum.pdf|accessdate=2008-05-03
* [http://www.youtube.com/watch?v=S42lLTlnfZc Video of Wilberforce pendulum oscillating] , by Berkeley Lecture Demonstrations, YouTube.com, retrieved April 25, 2008
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