Magnetic Torsional Pendulum Demonstrates Forced Resonance, Parametric Resonance, and Parametric Amplification
Researchers have developed a magnetic torsional pendulum apparatus that experimentally demonstrates three distinct resonance phenomena—forced resonance, parametric resonance, and parametric amplification—within a single system. The device uses a permanent magnet suspended by wires and driven by Helmholtz coils, with a wireless gyroscope for real-time angular velocity measurements. The platform is designed for undergraduate laboratory instruction and provides a low-cost, accessible way to study oscillation theory and nonlinear dynamics.
A new experimental apparatus combines a permanent magnet suspended by thin wires with externally applied magnetic fields from Helmholtz coils to create a unified platform for investigating three resonance mechanisms. By independently controlling a direct driving field and a periodically modulated bias field, the system can operate in three distinct modes: ordinary forced oscillations, parametric excitation, and phase-sensitive parametric amplification. A miniature wireless gyroscope embedded in the pendulum bob enables direct measurement of angular velocity and real-time data acquisition. The researchers derived a unified equation of motion describing all three operating regimes and validated their theoretical predictions through experimental measurements and numerical simulations. The apparatus demonstrates characteristic features of all three phenomena while illustrating how nonlinear effects influence system dynamics. The design emphasizes simplicity, low cost, and visible motion, making it suitable for advanced undergraduate laboratory education.
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- arXiv physicsCenter
A Magnetic Torsional Pendulum for Exploring Forced Resonance, Parametric Resonance, and Parametric Amplification
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