In this paper we investigate vibrations of discrete and continuous systems with damping of the MASING type. For free vibrations the method of the slowly varying amplitude and phase shows good agreement with numerical results, especially if the damping is small. The equations resulting from this method allow a faster identification of the parameters of a physical model. First, a single degree of freedom system is studied. Explicit formulae are obtained for the changing amplitude and frequency. The results are useful since damping laws of the type under consideration are well suited to describe the energy dissipation in a variety of real structures. In the second part we consider a one dimensional continuum with a distributed MASING model. An explicit formula is found for the dissipated energy per cycle and wavelength in standing waves.

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