Carrier Period as a Temporal Signature in Coupled Repelling Magnetic Pendula: An Entry Point to Active Magnetic Oscillation (AMO)

Version 1.3 revised preprint. This version refines the manuscript’s scope and framing, strengthens the error-analysis section, adds conflict-of-interest and data-availability statements, and aligns the paper more explicitly around the observational claim of carrier-period invariance within the detectable envelope.

This preprint documents the measured carrier period (Tc)(T_c)(Tc) in a coupled system of repelling magnetic pendula within the Active Magnetic Cradle (AMC) configuration, using Case Study 3 as the focal dataset. It presents the experimental setup, Tracker-based motion analysis workflow, peak-detection method, histogram results, and reproducibility materials.

Publicly available supporting materials

• Extracted Tracker dataset: 10.5281/zenodo.16236175
• 60 FPS source video: 10.5281/zenodo.17281410
• Python peak-detection and histogram scripts: 10.5281/zenodo.17472105

This version should be read as an observational and reproducibility-focused preprint. It is intended to document the measured carrier-period behavior under the stated experimental conditions and to support independent inspection and replication.

This paper is designed to be used alongside the public Python script AMC_Carrier_Period_PeakAnalysis_CS3.py, and the corresponding Case Study 3 Dataset dataset hosted on Zenodo.

Understanding the histogram: Lower interval values are retained in the plotted distribution for transparency of the extracted peak structure, but the y are not treated in this manuscript as part of the dominant carrier-period estimate. In the accompanying script, peak selection is stabilized using prominence-based detection and minimum-distance thresholding to reduce sensitivity to minor local fluctuations. The reported carrier period is based on the dominant clustered interval band identified under those conditions. Small variations within that band are documented in the manuscript as structured observational features within the detectable envelope; their formal characterization is beyond the scope of this version.

Related Works:
Measured Carrier-Period Invariance Within the Detectable Envelope of a Coupled Repelling Magnetic Pendulum System: 10.5281/zenodo.20100886
Measured 2.5-Cycle Energy Handover in a Coupled Repelling Magnetic Pendulum System: 10.5281/zenodo.20370420
Nonlinear Equations of Motion and Multipole Expansion for Active Magnetic Oscillation: 10.5281/zenodo.20649129
AMC Dataset — Unified Magnetic Field and Kinetic Energy Dataset - PHASE 2 - (Identical AMC model used in Case Study 3): 10.5281/zenodo.17741166
Active Magnetic Cradle — Case Study 3 Source Video Used to Generate Dataset DOI 10.5281/zenodo.16236175: 10.5281/zenodo.17281409
Python peak-detection and histogram scripts for carrier-period extraction (Case Study 3): 10.5281/zenodo.17472105
ResearchGate profile / discussion layer: https://www.researchgate.net/publication/405103482_Carrier_Period_as_a_Temporal_Signature_in_Coupled_Repelling_Magnetic_Pendula_An_Entry_Point_to_Active_Magnetic_Oscillation_AMO