a) A pair of poles of a second order system are located at - 2 ± 5j . Provide a sketch illustrating their locations on the Re-Im plane. Determine the natural frequency wn and the damping ratio and...

Extracted text: a) A pair of poles of a second order system are located at - 2 ± 5j . Provide a sketch illustrating their locations on the Re-Im plane. Determine the natural frequency wn and the damping ratio and indicate the values on your sketch. b) If the system is subjected to a unit step input, estimate (i) rise time and (ii) overshoot as a percentage of the steady-state value c) If specifications are to be improved (ie. faster response and lower overshoot), show the permissible region in the Re-Im plane where the poles can be located using your sketch created in part (a) (you can use separate sketches) d) (Note: This question is independent of parts a, b, and c) For a second order system, sketch the locations of Five pairs of poles that represent (i) underdamped (ii) overdamped (iii) critically damped (iv) overdamped and (v) unstable systems, and label the poles on your sketch