The oscillation model on networks offers a powerful way of describing the user dynamics in online social networks. In general, the damping effect of the oscillation model should depend on the eigenfrequency of the oscillation mode, as is true for many oscillation phenomena around us. This work starts with the frequency-dependent damping effect from which we propose a method for estimating the damping coefficient, that is the strength of the damping effect, from the observed oscillation dynamics.