Relativistic Springs

TL;DR

This paper introduces a relativistic spring model that incorporates relativistic momentum and delayed force effects, revealing significant deviations from classical harmonic oscillator behavior in energy conservation and period independence.

Contribution

It presents a novel relativistic spring model combining momentum and delay corrections, analyzing their individual and combined impacts on oscillator dynamics.

Findings

Relativistic momentum preserves energy but affects period independence.

Delayed force law maintains period independence but breaks energy conservation.

Combined corrections lead to increasing amplitude and period over time.

Abstract

Here we develop a model for the relativistic spring. We examine the effects of revising the simple harmonic oscillator to include relativistic momentum and a delayed force law. These corrections alter two of the most significant features of the simple harmonic oscillator: energy conservation and a constant period independent of initial conditions. The relativistic momentum correction, while preserving energy conservation, does not have period independent of initial conditions. The delayed force law, while preserving period independence, does not conserve energy. Applying both corrections creates a solution with increasing amplitude and increasing period, a result that is very different from the traditional simple harmonic oscillator.