A note on the energy transfer in coupled differential systems

TL;DR

This paper investigates how energy transfer occurs in a coupled linear differential system with opposing damping and antidamping effects, focusing on the influence of the coupling parameter on system behavior.

Contribution

It provides an analysis of the energy transfer dynamics in a coupled system with dissipation and antidissipation, highlighting the role of the coupling parameter.

Findings

Energy transfer depends on the coupling parameter b.

Damping and antidamping effects influence system stability.

The system exhibits different behaviors based on the balance of damping mechanisms.

Abstract

We study the energy transfer in the linear system $$ \begin{cases} \ddot u+u+\dot u=b\dot v\\ \ddot v+v-\epsilon \dot v=-b\dot u \end{cases} $$ made by two coupled differential equations, the first one dissipative and the second one antidissipative. We see how the competition between the damping and the antidamping mechanisms affect the whole system, depending on the coupling parameter $b$.