Fractional damped-coupled oscillator of two identical masses

Abstract

An oscillator made up of two identical masses with Hooke’s law interaction and time-fractional order damping term is studied. The general solution is obtained using the Laplace Transform method and a method previously used by Burov and Barkai for the single oscillator problem. Transitions between different behaviors are observed when the position versus time is plotted as the frequency varies. Three regimes for the frequency are found out. The first region depicted monotonous behavior. The next one is a non-monotonous region. The third one is an oscillatory decay which is akin to an under-damped motion.