Discussion
The close loop transfer function of for a unity feedback system is \(C(s)/R(s) = K/(s^2 + 4s + K)\).
The correct statement is:
Answer: A
The characteristic equation of the closed loop system is \(s^2 + 4s + K = 0\), with roots
\[ s = \frac{-4 \pm \sqrt{16 - 4K}}{2} \]
For \(K = 4\) the discriminant is zero, so
\[ s_1 = s_2 = -2 \]
The roots are real and equal (repeated), at the same point \(-2\) on the negative real axis, and the system is critically damped. The roots are not on the imaginary axis, which would need no \(s\) term, and the value \(-6\) in the last option is wrong. The answer is option A.
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