(b) Figure 2.1 shows a rotational mechanical system with an input torque, T(t) that produces an angular displacement of \(\theta(t)\).
i. Derive the transfer function of the given system, \(\theta(s)/T(s)\). (5 marks)
ii. Based on the system shown in Figure 2.1, solve the values of J and D to yield 20% overshoot and a settling time at 2% error band of 2 seconds. (16 marks)
K = 5 N-m/rad
Figure 2.1 Rotational mechanical system.