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The damping ratio can be found for any two adjacent peaks. This method is used when n=1 and is derived from the general method above:
: <math> \zeta = \frac{1}{\sqrt{1 + (\frac{2\pi}{\ln (x_0/x_1)}})^2}
where ''x''<sub>''0''</sub> and ''x''<sub>''1''</sub> are any two successive peaks.
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And for system <math> \zeta << 1 </math> (not too close to the critically damped regime, where <math> \zeta = 1 </math>).
: <math> \zeta = \frac{\ln (x_0/x_1)}{2\pi}
==Method of fractional overshoot==
The method of fractional overshoot can be useful for damping ratios between about 0.5 and 0.8. The fractional overshoot ''OS'' is:
: <math> OS = \frac{x_p - x_f}{x_f}
where ''x''<sub>''p''</sub> is the amplitude of the first peak of the step response and ''x''<sub>''f''</sub> is the settling amplitude. Then the damping ratio is
: <math> \zeta = \frac{1}{\sqrt{1 + (\frac{\pi}{\ln OS}})^2}
== See also ==
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