Parametrically Excited Anharmonic Oscillator

Abstract

Earlier [0] analyzed the behavior of the "dynamic point" -the harmonic oscillator. But there are phenomena for which even the damped harmonic oscillator is not elementary, but primitive. ELEMENTARY is an oscillator, which was previously called simply parametric, but, as shown in this work, strictly speaking, should be called parametrically excited anharmonic oscillator. As the analysis showed, this oscillator has stationary solutions for a harmonic oscillator at a doubled resonant frequency and for only one strictly defined level of attenuation, the deviation from which leads to a catastrophic increase, or to full cancellation of the oscillations. As shown in the elementary model, the doubled resonant frequency of the excitation occurs with orthogonal (transverse) oscillation at the frequency of the longitudinal resonance. This analysis was done to describe the anomalous non-transmission band in boron nitride.