Taking the results from the time constant of the exponential decay and the ringing frequency, the two vibrational parameters can be determined.
Using Equation 3 of the Free Vib. Sys. Parameters page and Equation 2 of the Ringing Frequency page it can be shown that the natural frequency is given by:
(1)
and the damping ratio by:
(2)
as functions of the time constant, , and the ringing frequency, .