2012/05/13 by Dylan P. Clark, Clark, Dylan P.
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Particle Accelerators and Free-Electron Lasers #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.1205.2823
openalex publication_date 2012/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.