(Solved): a. Sketch the root locus. b. Find the j-axis crossing and the gain, K, at t ...

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a. Sketch the root locus. b. Find the $$j?$$-axis crossing and the gain, $$K$$, at the crossing. c. Find the real-axis breakaway to two-decimal-place accuracy. d. Find angles of arrival to the complex zeros. e. Find the closed-loop zeros. f. Find the gain, $$K$$, for a closed-loop step response with $$30\%$$ overshoot. g. Discuss the validity of your second-order approximation.