Routh-Hurwitz Stability Criterion: Solving Feedback Control Systems Homework

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Homework Statement

http://img24.imageshack.us/img24/9028/72841137.jpg

Homework Equations

Routh-Hurwitz Stability Criterion

The Attempt at a Solution

For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough

How would I approach the second question though? Any starters would be sincerely appreciated.

 

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Homework Statement

http://img24.imageshack.us/img24/9028/72841137.jpg

Homework Equations

Routh-Hurwitz Stability Criterion

The Attempt at a Solution

For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough

How would I approach the second question though? Any starters would be sincerely appreciated.

You got the value K = 1 by making the line $$s^1$$ equal to zero. Now, you form an auxiliary equation with the coefficients of the $$s^2$$ line. The roots of the auxiliary equation are also roots of the characteristic equation. Solve it and you get two imaginary roots, whose module is the oscillation frequency when K = 1.