Given the rotational system shown in Figure P4.23, do the following: a. Using the transfer function you derived for that system, G(s) = 1

Given the rotational system shown in Figure P4.23, do the following:

a. Using the transfer function you derived for that system, G(s) = Θ₁(s)/T(s), where Θ₁(s) is the angular displacement of the first shaft, find the value of n = N₁/N₂ that yields a settling time of 10 seconds for a step input in torque.

b. If this rotational system is the controlled unit, G(s), in the feedback system of Figure P5.51, find the values of ζ; ω_n, %O.S., and T_s for a controller gain K = 4 N-m/rad and r(t) = u(t) radians.

R(s). E(s) C(s) K G(s) FIGURE P5.51