Question

Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response system. and write your answer in standard format 17.7831+ jo d+jot where the time Consider system where Hju) = constants aret, 0.08 ms, τ,-8ms and τ,-0.8 ms. (0 Sketch the individual elements Bode Amplitude Responses. (i) Calculate the amplitude response of the second order system where the (b) -n) , frequency of the input is 85 Hz. (c) Consider a system whose individual components are drawn in the accompanying Bode Plot 0) Sketch the combined Bode Amplitude Response. (ii) Write out the frequency response of the system, something like the form of 17.7831+jo,+jor,) (l+jor,) H(jo) Note you will first to calculate the four time constants. τυΤ,t,t.that correspond to the cut-off frequencies, fc,ー10Hz.fc2=30Hz.fc,-70Hz andfc, 150Hz

Answer 1

Gi en Ihnl h(t): 4000e.北3000 est t>o , We at 6-a Lt4000 ept_ 3000 e 3000 4000 (6 40) (St 0 6) 4000 3000 lo0o4SHc) -306+0-5) (6to6Y 6+0 S) lDoo 54 24-15 (6406) (510) to 0 6+0 61 6+0.5) o(0 000XoQ