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An idealized free‐vibration experiment is analyzed on the basis of the theory of infinitesimal linear viscoelasticity. The resulting motion can be expressed as a sum of terms, of which some are damped sinusoidal waves while others are negative exponentials in time. For some three parameter models of viscoelastic behavior, the results of this theory are compared with those of the usual treatment which leads to a simple damped sinusoidal wave.