We use the theory of resonantly damped quasi-mode kink oscillations together with observational estimates of periods and damping times of transversal coronal loop oscillations to extract information on physical parameters in oscillating loops. A parametric numerical study of the quasi-mode period and damping as a function of several equilibrium parameters is used to perform and inversion to obtain those equilibrium models that reproduce the observed period and damping rates, for a set of 11 loop oscillation events. Both the period and the damping rate are used and the equilibrium Alfvén speed comes into play. An upper limit to the Alfvén speed has been derived for 9 of the 11 analysed events.
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