Relativistic Springs
  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. 
Dylan P. Clark
physics.class-ph