timeresponse12

# timeresponse12 - Time Response QUESTION 12 For each pair of...

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Time Response Q UESTION 12 For each pair of second–order system specifications below, find the pole locations. a. % OS = 20% and T s = 8 s b. % OS = 5% and T p = 2 s c. T s = 4 s and T p = 1 s For % OS = 20%, the damping ratio is 2 2 2 2 % 20 ln ln 100 100 0.4559 % 20 ln ln 100 100 OS OS ζ π - - = = = + + (1) For T s = 8 s and the damping ratio given in equation (1), the natural frequency is ( 29 4 rad 1.097 8 0.4559 s n ϖ = = (2) Therefore, the poles are located at 2 1 0.5001 0.9764 n n j j ζϖ - ± - = - ± . For % OS = 5%, the damping ratio is 2 2 2 2 % 5 ln ln 100 100 0.6901 % 5 ln ln 100 100 OS OS - - = = =

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timeresponse12 - Time Response QUESTION 12 For each pair of...

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