A certain system has two coupled subsystems. One subsystem
Chapter , Problem 8.31(choose chapter or problem)
A certain system has two coupled subsystems. One subsystem is a rotational system with the equation of motion:
\(50 \frac{d \omega}{d t}+10 \omega=T(t)\)
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 \(i_{f}\) in amperes is
\(0.001 \frac{d i_{f}}{d t}+5 i_{f}=v(t)\)
where v(t) is the voltage applied to the motor. The motor torque constant is \(K_{T}=25 \mathrm{~N} \cdot \mathrm{m} / \mathrm{A}\). Obtain the damping ratio \(\zeta\), time constants, and undamped natural frequency \(\omega_{n}\) of the combined system.
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