Non-harmonic response of relativistic particle to driving harmonic force

We consider the properties of one-dimensional oscillations of a relativistic particle under a driving harmonic force. It is found that in the general case the speed oscillations are an infinite sum of odd sinusoidal and even cosinusoidal waves. In the limiting case of the ultra-relativistic particle, they represent a square wave. There is also the oscillation suppression for large values of the force amplitude and particular values of its initial phase. In this case, the particle performs only drift motion. The topic is addressed to undergraduates studying the applications of the theory of oscillations.

Keywords
Driven oscillator; relativistic particle; Fourier series; square wave