A magnet suspended by a spring will display simple harmonic motion when displaced. If the magnet oscillates within a coil connected to a resistor, its motion will be damped. Investigate the factors that affect the damping.
*20.6b Ex1: ON11 P41 Q3 Oscillating Magnet Damping | A2 Induction | CAIE A Level Physics(youtube, ETphysics, 02.02.2021), https://youtu.be/ElEMzE06r8Y *Wikipedia: Magnetic damping, https://en.wikipedia.org/wiki/Magnetic_damping *Wikipedia: LC circuit, https://en.wikipedia.org/wiki/LC_circuit *Wikipedia: Electromagnetic induction, https://en.wikipedia.org/wiki/Electromagnetic_induction *B. Cadiou, C. Stephan, A. Renoult, and G. Michon. Damping adjustment of a nonlinear vibration absorber using an electro–magnetomechanical coupling. J. Sound Vib. 518, 116508 (2022), https://doi.org/10.1016/j.jsv.2021.116508 *M.-H. Kwon and H.-M. Choi. Study on the underdamped oscillation of a mass-spring system subject to electromagnetic induction. New Physics: Sae Mulli 2, 62, 128-134 (2012), https://doi.org/10.3938/NPSM.62.128 *G. Donoso, C. L. Ladera, and P. Martín. Magnetically coupled magnet–spring oscillators. Eur. J. Phys. 3, 31, 433-452 (2010), https://doi.org/10.1088/0143-0807/31/3/002
*A. Singh, Y. N. Mohapatra, and S. Kumar. Electromagnetic induction and damping: Quantitative experiments using a PC interface. Am. J. Phys. 70, 4, 424-427 (2002), arXiv:physics/0111016 [physics.ed-ph], https://doi.org/10.1119/1.1446859 How resistance in coils affects the damping of oscillations of a magnet through them (physics.stackexchange.com, Aug 25, 2018), https://physics.stackexchange.com/questions/424726/how-resistance-in-coils-affects-thedamping-of-oscillations-of-a-magnet-through
*A. Fow and M. Duke. Determining the characteristics of a passive linear electro-magnetic damper for a lightweight vehicle (waikato.ac.nz), https://researchcommons.waikato.ac.nz/server/api/core/bitstreams/a89ae679-a936-46a1-a43af274c9ab4353/content
[Sneller10] A. Sneller, and B. Mann, On the nonlinear electromagnetic coupling between a coil and an oscillating magnet. J. Phys. D: Appl. Phys. 43, 295005, 2010. https://iopscience.iop.org/article/10.1088/0022-3727/43/29/295005
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Notice the equivalent circuit of the part related to electromagnetic induction and the effect from changing the equilibrium position of the magnet.
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[Bancel99JPhysD] F. Bancel, Magnetic nodes. J. Phys. D: Appl. Phys. 32, 2155–2161, 1999. https://iopscience.iop.org/article/10.1088/0022-3727/32/17/304 https://www.researchgate.net/publication/353552839_Analytical_Solution_of_the_Euler-Poinsot_Problem
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Useful if the geometry and size of the magnet needs to be taken into account.
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[PIER09] R. Ravaud and G. Lemarquand. Magnetic field produced by parallel-periodic of various and uniform polarization . Progress In Electromagnetics Research, PIER 98, 207-219, 2009, https://www.jpier.org/PIER/pier.php?paper=09091704
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Useful if the geometry and size of the magnet needs to be taken into account.
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Study the temporal behaviors of oscillation amplitude (or the maximal speed of the magnet in each swing), the induced emf/current (across/through the coil or the load resistor).
Intuitive factors
What role does the load resistance (of the coil) play?
How can we justify the equivalent circuit of the coil (sneller10, Fig. 1b) is a good model? You should check it through changing the value of 𝑅L.
𝑅L: load resistance of the coil.
𝑅i: inner resistance of the coil.