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Consider the forward loop transfer function in the sampled-data system as:
G(s) = K / s(s + 4)
(a) Determine the corresponding z -transform G(z) and the characteristic equation for this system.
(b) Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s.
(c) Construct the root locus plot for this system.
solve the characteristic equation above for the roots m1 and m2. hint you may need to solve by factoring or by using
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Factor the given algebraic expression.
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