Question

(a) Given the second-order frequency response function: H(j \omega)=\frac{100}{(j \omega)^{2}+51 j \omega+50} (i) Analytically determine the straight line approximations (asymptotes) of the Bode Log-Magnitude plot of the frequency response function. (ii) Sketch the Bode magnitude (dB) of the frequency response function, clearly labeled, and indicate the frequency () where the OdB-line is crossed on your sketch. You are not required to sketch the phase. An LTI system subjected to an input x() has a response y(t), and its frequency response function is: H(j \omega)=\frac{2}{\frac{1}{3}(j \omega)^{2}+\frac{5}{3} R j \omega+2} \text { where } R \text { is a resistance }(\Omega) \text {. } For what range of values of the resistance R is the system under damped? \text { (ii) If } R=1 \Omega \text {, what is the impulse response, } h(t) \text { of the system? } \text { (ii) If } R=1 \Omega \text {, what is the impulse response, } h(t) \text { of the system? } \text { (iii) If } R=1 \Omega \text {, what is the step response, } s(t) \text { of the system? }

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