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The characteristic equation of a control system is s(s^2+ 6s+13)+K=0. The value of k such that the characteristic equation has a pair of complex roots with real part -1 will be :

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The characteristic equation of a control system is s(s^2+ 6s+13)+K=0. The value of k such that the characteristic equation has a pair of complex roots with real part -1 will be :

(a) 10

(b) 20

(c) 30

(d) 40

I had been asked this question during an interview.

My question is based upon Time Response of Second Order Systems topic in portion Time Response Analysis, Design Specifications and Performance Indices of Control Systems

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Right answer is (b) 20

Best explanation: The characteristic equation is considered and the values of G and w are calculated and further the value of k can be calculated.

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