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Updated: Sep 11, 2025
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Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
Published on: September 21, 2017
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Nonlinear dynamics of a ball bouncing on a vibrating ferrite rod
Ke Li1,2, Kangqi Liao3, Feng Song3
1The Experimental High School Attached to Beijing Normal University, Beijing 100032, China.
Physical Review. E
|August 19, 2025
Summary
This study examines a ball bouncing on a ferrite rod within an alternating magnetic field. Our findings reveal a frequency doubling effect influencing the ball's rebound velocity distribution, with potential for periodic motion.
Area of Science:
- Physics
- Magnetism
- Nonlinear Dynamics
Background:
- Investigating the complex interactions between magnetic fields and mechanical systems.
- Understanding the phenomenon of magnetostriction in ferrite materials.
Purpose of the Study:
- To analyze the dynamics of a ball bouncing on a ferrite rod in an alternating magnetic field.
- To derive and validate the probability distribution function (PDF) of the ball's rebound velocity.
Main Methods:
- Utilizing linear magnetostriction theory to model rod vibrations.
- Analytical determination of the rebound velocity PDF.
- Validation through numerical simulations and experimental results.
Main Results:
- The derived PDF accurately predicts high-velocity rebound distributions.
- Minor discrepancies at low velocities due to nonlinear relative velocity.
- Simulations indicate the ball can enter a periodic motion 'locking region'.
Conclusions:
- Linear magnetostriction theory provides a strong basis for understanding the system's dynamics.
- The frequency doubling effect significantly impacts rebound velocity.
- The system exhibits complex behaviors, including periodic motion.
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