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Fig.5 23   Frequency-response parameters.
LINEAR SYSTEMS, THEORY, AND DESIGN: A BRIEF REVIEW       485
       To determine the peak amplitude M p and the corresponding frequency COp, take
 the squares on both sides ofEq. (5.147), differentiate with respect to to, and equate
the resulting expression to zero to obtain
                                                               1
            (5.148)
                                 Mp = 2"j2_~
                                     (Op = tOn,n-=2T7-                          (5.149)
Equations (5.148) and (5.149) show that Mp and COp of the closed-loop frequency
response are directly related to the damping ratio C. The percent overshoot Os and
damping ratio < are related through Eq. (5.75), which is reproduced here in the
following:
                                                                                                         - ~,( Os/l00)
　
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