This paper describes an inexpensive, classroom experiment that allows students to quantitatively investigate resonance using a hacksaw blade. The blade clamped to the edge of a table forms a cantilever that may vibrate at any of a number of preferred frequencies. A small cylindrical magnet is fixed to the saw blade. An electromagnetic coil powered by a frequency generator causes large-amplitude vibrations of the saw blade at the resonant frequencies. Vibrations of a similar system, a vibrating car antenna, have been discussed by Newburgh and Newburgh.1 The dramatic increases in the oscillation amplitude are both instructive and fascinating. Analogies may be drawn to systems ranging from a child on a swing to the Tacoma Narrows bridge.

Topics
Signal generators, Education
1.
Ronald
Newburgh
 and
G. Alexander
Newburgh
, “
Finding the equation for a vibrating car antenna
,”
Phys. Teach.
38
,
31
–
34
(Jan.
2000
).
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2.
Somdev
Tyagi
and
Arthur E.
Lord
Jr., “
Simple and inexpensive apparatus for Young's modulus measurement
,”
Am. J. Phys.
48
,
205
–
206
(March
1980
). This article describes the use of an audio speaker to drive a small wire.
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3.
Keith
Turvey
, “
An undergraduate experiment on the vibration of a cantilever and its application to the determination of Young's modulus
,”
Am. J. Phys.
58
,
483
–
487
(May
1990
). This paper also describes the use of an electromagnet to drive a steel blade; however, it does not employ the small permanent magnet that makes it possible to investigate non-ferromagnetic beams.
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4.
The small coil electromagnet that I use is no longer available from Frey Scientific. However, similar coils from Frey should work as well. Transformer coils, Catalog #96584553 and #96584556; large electromagnet, Catalog #96564682; electromagnetic coils (set of six), Catalog #96562912. Frey Scientific, P.O. Box 8101, Mansfield, OH 44901; http://www.freyscientific.com.
5.
I use an NdFeB cylindrical magnet, ¼ in (6 mm) in diameter and ¼ in (6 mm) tall. The magnet is available from Forcefield, 2606 W. Vine Drive, Fort Collins, CO 80521; http://www.wondermagnet.com.
6.
Alternate methods suggest themselves. One might try to measure the deflection with a motion detector. A small mirror could be fixed to the end of the blade. A laser beam reflected from the mirror could form an optical lever to magnify the blade oscillations. A second small magnet at the end of the blade could induce an electrical signal in a second pick-up coil.
7.
See, for example, Richard Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1964), Vol. II, pp. 38-9 and 38-10.
8.
Depending on composition, typical values for the modulus of elasticity range from 100 GN/m2 for iron to 200 GN/m2 for steel. See, for example, Douglas Giancoli, Physics (Prentice Hall, Upper Saddle River, NJ, 1980), p. 254.
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© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers
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