Resonance is typically studied in the context of either a pendulum or a mass on a spring. We have developed an apparatus that enables beginning students to investigate resonant behavior of changing magnetic fields, in addition to the properties of the magnetic field due to a wire and the superposition of magnetic fields. In this resonant system, a compass oscillates at a frequency determined by the compass's physical properties and an external magnetic field. While the analysis is mathematically similar to that of the pendulum, this apparatus has an advantage that the magnetic field is easily controlled, while it is difficult to control the strength of gravity. This apparatus has been incorporated into a teaching module on magnetic resonance imaging.

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See supplementary material at http://dx.doi.org/10.1119/1.4928177 for Supplement 1 which discusses the validity of the assumptions made when calculating the theoretical magnetic field strength at the compass in Sec. III B. Supplement 2 gives the details of the theoretical calculations shown in Fig. 5. The third supplement is a collection of videos showing compasses being put into resonance by tapping the switch. The fourth supplement is the MRI activity instructions written as part of the Modern Miracle Medical Machines project at Kansas State University, which incorporates the apparatus discussed in this article.
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The instructions for this activity are available in the online supplement for this article (Ref. 12) and also at the Modern Miracle Medical Machines web site, <http://web.phys.ksu.edu/mmmm/>.
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The Simplified MRI visualization is available at the PhET Project web site, <http://phet.colorado.edu/en/simulation/mri>.

Supplementary Material

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