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Question: q1 20 marks for the 2nd order system with the...

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Q.1 (20 marks) For the 2nd order system with the following transfer function 4 (a) G(s) s2 +2s+4 (b) G(s+90s+900 (c) G(s)- 16 (d) G)323 s2+90s+900 s2+8s+16 S2+25 For each system (a-d): (1 ). Determine the un-damped natural frequencies ωη and damping ratio (2). Find the roots(solutions) for the characteristic equation and draw them on the s- plane. Based on the roots, determine the system type into one of the following categories (under-damped, critically damped, un-damped, or over-damped) (3). Analytically determine the time response of each system under a unit step input (Using partial fraction decomposition technique, and you may find inverse Laplace transformation in the attached table). Check out the partial fraction expansion video it needed. (4). Determine the system unit step response using Matlab Simulink, and compare the response with the response obtained in (3) by plotting the results on the same figure. (Matlab fplot function may be useful for plotting mathematical expressions.)

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