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Consider the root locus for a unity-gain negative feedback system having the cha...

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Consider the root locus for a unity-gain negative

feedback system having the characteristic equation 

, where k denotes the compensator

gain of

the forward path transfer function. 

Let k = kmarginal > 0

be the

value of the gain at which the branches of the root locus intersect the imaginary axis. 

Let s = j wmarginal be the point on the imaginary axis at which one of the branches of the root locus intersects the positive half of the imaginary axis.

The value of wmarginal =  

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