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The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function G(s) = K / ((s−1)(s−4)) is

1. 1
2. 2
3. 5
4. 9

Correct answer: 2

Solution

At the breakaway point of the root locus, the gain K can be determined by analyzing the characteristic equation and the conditions for stability. For this system, the calculations show that the gain at the breakaway point is 2, which corresponds to the specific configuration of the poles and the feedback system.

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