The equations:
Let the Damping Ratio be z and the amplitude
of two successive peaks be A1 and A2.
ln (A1 / A2) = Pi * z / sqrt ( 1 - z**2)
z = 1 / sqrt {1 + [Pi / ln(A1 / A2)]**2}
Q = 0.5 / DampingRatio
("STO1" for A1 and "STO2" for A2.)
See also W. Bauer's applet for an animation of a damped oscillator.