A single-loop negative feedback system has a loop transfer function

(a) Sketch the root locus for 0 ‰¤ K ‰¤ ˆž to indicate the significant features of the locus.
(b) Determine the range of the gain K for which the system is stable.
(c) For what value of K in the range K ‰¥ 0 do purely imaginary roots exist? What are the values of these roots?
(d) Would the use of the dominant roots approximation for an estimate of settling time be justified in this case for a large magnitude of gain (K > 50)?

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L(s)