An irreversible transformation of mechanical into thermal energy takes place during the motion of a damped harmonic oscillator, with the result that the level of the total mechanical energy of the system, as a first approximation, decays exponentially with time. A detailed description of this decrease, however, is not usually supplied in textbooks of classical mechanics or general physics. As Karlow has recently pointed out, the negative-exponential decay is modulated by a sequence of energy ripples, owing to the dissipation rate being not constant during the motion. Up to now, the analysis of this behavior has been based only on theoretical considerations; in this work we present the corresponding experimental evidence based on a couple of laboratory demonstrations that use an electrical RLC circuit and a hydrodynamically damped mechanical pendulum.