When two identical simple harmonic oscillators are coupled by a linear spring that has a spring constant the system has two resonant frequencies. There is a resonance at their natural frequency, when the oscillators oscillate in phase and a resonance at the frequency when the oscillators are 180° out of phase. These oscillations are referred to individually as the symmetric and antisymmetric modes or collectively as the normal modes. The frequencies are called the normal frequencies.
REFERENCES
1.
Stephen T. Thornton and Jerry B. Marion, Classical Dynamics of Particles and Systems, 5th ed. (Thomson Brooks/Cole, Belmont, 2004).
2.
A.P. French, Vibrations and Waves (W.W. Norton and Company Inc., New York, 1971).
3.
Charles A.
Sawicki
, “Inexpensive coupled-oscillations demonstration
,” Phys. Teach.
39
, 172
–173
(March 2001
). Describes a system of oscillators with adjustable magnetic coupling.4.
Antonio
Carnevali
and Cynthia L.
Newton
, “Coupled harmonic oscillators made easy
,” Phys. Teach.
38
, 503
–505
(Nov. 2000
). Presents a simplifying procedure that avoids the use of the FFT.5.
Norris W.
Preyer
, “The coupled harmonic oscillator: Not just for seniors anymore
,” Phys. Teach.
34
, 52
–55
(Jan. 1996
). Analyzes quantitatively the motion of coupled oscillators using the FFT and spreadsheet modeling.6.
Bernard J.
Weigman
and Helene F.
Perry
, “Experimental determination of normal frequencies in coupled mechanical oscillator systems using fast Fourier transforms: An advanced undergraduate laboratory
,” Am. J. Phys.
61
, 1022
–1027
(Nov. 1993
). Describes the use of a force transducer for data collection and the use of the FFT to analyze the motion of a coupled oscillator. The description is mathematical.7.
Frank G.
Karioris
and Kenneth S.
Mendelson
, “A novel coupled oscillation demonstration
,” Am. J. Phys.
60
, 508
–513
(June 1992
). Describes a “fun” system comprising a rotating rod and two support springs. The coupling is between the vertical and rotational motions of the rod.8.
David L.
Wallach
, William
Beatty
, Karl
Beisler
et al., “The effect of the mass of the center spring in one-dimensional coupled harmonic oscillators
,” Am. J. Phys.
56
, 1120
–1123
(Dec. 1988
). Addresses the issue of the mass of the coupling spring in a system of two linear coupled oscillators.9.
PASCO Scientific Motion Sensor PS 2103, PASCO scientific, 0101 Foothills Blvd. Roseville, CA 957471; http://www.pasco.com.
10.
LabPro and Logger Pro are manufactured by Vernier Software and Technology, 13979 SW Millikan Way, Beaverton, OR 97005-2886; http://www.vernier.com.
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© 2006 American Association of Physics Teachers.
2006
American Association of Physics Teachers
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