For the system shown in Figure P8.11, do the following: a. Sketch the root locus. b. Find

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For the system shown in Figure P8.11, do the following:

a. Sketch the root locus.

b. Find the jω-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.

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