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When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
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Related Experiment Video

Updated: Jan 19, 2026

Fabrication of Magnetic Nanostructures on Silicon Nitride Membranes for Magnetic Vortex Studies Using Transmission Microscopy Techniques
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Magnetic Pendulum Arrays for Efficient ULF Transmission.

Srinivas Prasad M N1, Rustu Umut Tok1, Foad Fereidoony1

  • 1Department of Electrical and Computer Engineering, University of California, Los Angeles, USA.

Scientific Reports
|September 15, 2019
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Mechanical antennas, or

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Area of Science:

  • Electromagnetics
  • Mechanical Engineering
  • Communications Systems

Background:

  • Ultra Low Frequency (ULF) communication (300 Hz – 3 kHz) offers reliable, penetrating, and jam-resistant transmission for underwater and underground environments.
  • Electrically small ULF antennas (diameter < 1 meter) are highly inefficient due to fundamental radiation limits.
  • Mechanical antennas ('Mechtennas') are a recent proposal to enhance ULF radiation efficiency.

Purpose of the Study:

  • To propose and demonstrate a novel electromechanical system for efficient Ultra Low Frequency (ULF) radiation generation.
  • To validate the Magnetic Pendulum Array (MPA) concept for ULF communication applications.

Main Methods:

  • Development of a portable electromechanical system: the Magnetic Pendulum Array (MPA).
  • Experimental proof-of-concept demonstration of the MPA at 1.03 kHz.
  • Theoretical analysis and experimental validation of system performance.

Main Results:

  • The MPA demonstrated a significantly higher quality factor compared to conventional ULF coils.
  • The system achieved an order of magnitude higher transmission efficiency for ULF radiation.
  • Experimental results validated the theoretical predictions for the MPA's performance.

Conclusions:

  • The Magnetic Pendulum Array (MPA) offers a viable solution for efficient ULF communication.
  • The MPA concept is scalable for practical ULF applications.
  • This electromechanical approach overcomes the limitations of traditional small ULF antennas.