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Given the loop transfer function
G(s)H(s) = k/s(s+3)(s+4)(s+5)
(a) Sketch the root locus plot for G(s)H(s).
(b) What is the system gain at s = -1+ 2i?
(c) Calculate the settling time.
(d) Find the gain margin for the gain selected in part (b).
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basic properties on the inverse of laplace transform
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A) For a given integer n, if n 2 is divisible by 4, then n2 4 is divisible by 16. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement
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