Carrier Period Extraction in Coupled Magnetic Pendula of the AMC System (Case Study 3)

This document provides a standalone, reproducible methodology for extracting the carrier period (Tc) from coupled repelling magnetic pendula within the Active Magnetic Cradle (AMC) system. Using Case Study 3 (CS3) as the basis, it presents the peak detection workflow, waveform histogram generation, and implications for understanding waveform-like timing in Active Magnetic Oscillations (AMO). Comparisons to recent oscillator research are acknowledged where applicable.

This paper is designed to be used alongside the public Python script AMC_Carrier_Period_PeakAnalysis_CS3.py, and the dataset for CS3 Zenodo Dataset.

Understanding the Histogram: The lower interval values represent sub-harmonic or noise artifacts, and are not part of the dominant periodicity.They do not constitute the system’s carrier period (Tc). They’re filtered out in the script using prominence and minimum distance thresholds, but are still plotted to show transparency of raw data. The carrier period is not rigid like a crystal oscillator, it’s more like a band-limited waveform riding on a structured decay. The slight variation is expected and explained by the wavelet handover behavior and natural decay of energy between oscillators. Specifically the peak intervals oscillate within a tight band, approximately 0.310 s to 0.369 s, even though the average may land at 0.3162 s (A) and 0.3104 s (B). This spread is not noise — it’s a structural waveform signature, likely tied to: Phase delay between the magnets, Coupled oscillation modes and Amplitude-modulated decay envelopes.

The analysis supports the broader AMC Law framework by confirming quantized timing behaviors distinct from classical SHM.