This work shows that the complex dynamic viscosity eta*(omega) can be evaluated from experimental data of free damped oscillations (FDO) when upper and lower angular displacements measured in a plate-plate geometry are analyzed by Fourier series. We deduce the equation required to evaluate experimentally the dynamic functions of linear viscoelastic materials in FDO. Two loss tangents can be defined in FDO, which are not necessarily equal to tan delta(omega) of the forced oscillation test.