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A pendulum with a broken cylindrical symmetry: normal modes and beats
- Source :
- European Journal of Physics, European Journal of Physics, 2021, 43 (1), pp.015005. ⟨10.1088/1361-6404/ac1e7a⟩, European Journal of Physics, European Physical Society, 2021, 43 (1), pp.015005. ⟨10.1088/1361-6404/ac1e7a⟩
- Publication Year :
- 2021
- Publisher :
- IOP Publishing, 2021.
-
Abstract
- A pendulum, which has the cylindrical symmetry around its suspension wire, has two degenerate normal modes. We break this symmetry by putting a small magnet in the pendulum body and by running the pendulum in the presence of an inhomogeneous magnetic field. The force due to the magnetic field gradient modifies the equilibrium position and the spatial derivatives of this force define the normal modes of the pendulum with two different oscillation frequencies. We describe this system theoretically and we test these results by a series of experiments. This system provides a classical analogue of the degenerate perturbation theory in quantum mechanics.
- Subjects :
- 010302 applied physics
Physics
[PHYS.PHYS.PHYS-CLASS-PH]Physics [physics]/Physics [physics]/Classical Physics [physics.class-ph]
Classical mechanics
Normal mode
0103 physical sciences
Pendulum
General Physics and Astronomy
010306 general physics
01 natural sciences
ComputingMilieux_MISCELLANEOUS
Symmetry (physics)
Subjects
Details
- ISSN :
- 13616404 and 01430807
- Volume :
- 43
- Database :
- OpenAIRE
- Journal :
- European Journal of Physics
- Accession number :
- edsair.doi.dedup.....81fdb3e5d707ae0f530b8e907d97f5ce
- Full Text :
- https://doi.org/10.1088/1361-6404/ac1e7a