Subresonant solutions of the linear oscillator equation

TL;DR

This paper investigates the behavior of linear oscillators under almost periodic forces, revealing solutions that grow more slowly than resonant ones and analyzing how their amplitude depends on perturbation parameters.

Contribution

It introduces subresonant solutions for linear oscillators and analyzes their amplitude dependence on almost periodic perturbations.

Findings

Subresonant solutions grow more slowly than resonant solutions.

Amplitude of solutions depends on parameters of the perturbation.

Provides a mathematical framework for understanding slow-growing solutions.

Abstract

The behavior of a linear oscillator under the action of an external almost periodic force is investigated. The constructed solutions grow more slowly than the resonant ones. The dependence of the amplitude of growing solutions on the parameters of an almost periodic perturbation is calculated.