(Solved): 4) (25pts) For an underdamped continuous-time second order control system below a) Determine the c ...

4) (25pts) For an underdamped continuous-time second order control system below a) Determine the closed loop transfer function and step response of this system b) Digitize the system using sampling frequencies 5, 10 and 20 times \( \omega_{d} \) (damped natural frequency) of the continuous time system and obtain step responses for each case. c) Determine which sampling frequency would be a proper choice by comparing step responses. Comment on the result.