A certain armature-controlled dc motor has the
Chapter , Problem 8.32(choose chapter or problem)
A certain armature-controlled dc motor has the characteristic equation
\(L_{a} I s^{2}+\left(R_{a} I+c L_{a}\right) s+c R_{a}+K_{b} K_{T}=0\)
Using the following parameter values:
\(\begin{array}{rlrl} K_{b}=K_{T} & =0.1 \mathrm{~N} \cdot \mathrm{m} / \mathrm{A} & I & =6 \times 10^{-5} \mathrm{~kg} \cdot \mathrm{m}^{2} \\ R_{a} & =0.6 \ \Omega & L_{a} & =4 \times 10^{-3} \ \mathrm{H} \end{array}\)
obtain the expressions for the damping ratio \(\zeta\) and undamped natural frequency \(\omega_{n}\) in terms of the damping c. Assuming that \(\zeta<1\), obtain the expression for the time constant.
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