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solution11

solution11 - 1(a the response is the sum of the responses...

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1/. (a) the response is the sum of the responses to 10 u ( t ) and 20cos(50 t ) DC gain is -40dB = 0.01 response to 10 u ( t ) = (0.01)(10) = 0.1 at ω = 50 the gain is -20dB = 0.1 and the phase shift is about +85” response to 20cos(50 t ) = (0.1) 20cos(50 t + 85”) total response = 0.1 + 2cos(50 t + 85”) (b) The usual rules apply. Whenever the input is a sinusoidal the steady state output will be the input multiplied by some gain and shifted by some amount. at ω = 10000 the gain is -30dB = 0.0316 and the phase shift is about -89” the response is (0.0316)500sin(10000 t + (34 - 89)”) = 15.811sin(10000 t -55”) (c) From the slopes of the asymptotes and their intersections, it can be concluded that there is a zero with ω C = 5 and a pair of complex poles with ω N = 400. The height of the peak (above the intersection of the asymptotes) is about 20dB. The value of ζ can be calculated from this height. 05

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solution11 - 1(a the response is the sum of the responses...

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