Logarithmic decrement: Difference between revisions

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==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 ''{{math|OS''}} is:

: <math>\mathrm{ OS} = \frac{x_p - x_f}{x_f} </math>

where ''x''_''p'' is the amplitude of the first peak of the step response and ''x''_''f'' is the settling amplitude. Then the damping ratio is

: <math> \zeta = \frac{1}{\sqrt{1 + \left(
\frac{\pi}{\ln(\mathrm{OS})}}
\right)^2}} </math>

== See also ==