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1 nnR(s)−Response (dB)University of Wollongong MECH321 Autumn 2016 - Tutorial 7 Solution1. Calculate the DC gains (in dB) of the three systems described by the following transfer functions (2 Marks), 6ω2 G1 (s) =, G2 (s) =s2 + 2ζωns + w2s2 + 7s + 22(s + 3)(s2 + 2s + 3), G3 (s) =s(s + 1)(s2 + 9)(s2 + 2s + 4)Answer:G1(s →0) = 6 ⇒15.56 dB, G2(s →0) = 2.44 ⇒7.76 dB, G3(s →0) = 0 ⇒−∞2. For a suspected second order dynamic system the transfer function cannot be determined mathematically. Instead the magnitude plot of the transfer function G(s) = C(s)is experimentally measured and is given below, Magnitudeplotof thesecond ordersystem10 5 0 −5−10−15−20−25−30−35−40−45−50−5560 10−1100 101 102Frequency (rad/s)An A4 copy of this graph and an expanded graph showing the peak detail are available on e-Learning if needed. (a) Determine the damping ratio ζ, the natural frequency ωnand thebandwidth ωb of the system. (1 Mark)
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