Question: The characteristic equation for a control system is given by: [ (s+2)(s+4)(s+alpha)+K=0 ] To achieve a good dynamic behaviour, it is desired that damping ratio

The characteristic equation for a control system is given by:

\[
(s+2)(s+4)(s+\alpha)+K=0
\]

To achieve a good dynamic behaviour, it is desired that damping ratio $\xi=0.5$ and that the natural frequency $\omega_{n}=4 \mathrm{rad} / \mathrm{sec}$, determine $\alpha$ and $\mathrm{K}$.

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