A certain system has two coupled subsystems. One subsystem is a rotational system with the equation of motion:
50 dω/dt + 10ω = T(t)
Where T(t) is the torque applied by an electric motor, Figure 8.1.8. The second subsystem is a field-controlled motor. The model of the motor's field current if in amperes is
0.001dif/dt +5if = v(t)
Where v(t) is the voltage applied to the motor. The motor torque constant is KT = 25 N.m/A. Obtain the damping ratio ζ, time constants, and undamped natural frequency ωn of the combined system.