Note: continuous time signals x(t), time t = R+; and its Laplace transform result is (s)...

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Note: continuous time signals x(t), time t = R+; and its Laplace transform result is (s) where s Z. n (a) Prove the following ODE is linear. azy (i) i=0 = U (b) For the following second order ODE: + 2wn y + w / Y = u, y(0) = Yo, y(0) = Vo, express the Laplace transform result Y(s) in terms of yo, vo, and U(s). Write out the transfer function G(s) and find its poles and zeros for the following four conditions: $ = 0, & (0, 1), that wn > 0. = 1 and, 1. Note Note: continuous time signals x(t), time t = R+; and its Laplace transform result is (s) where s Z. n (a) Prove the following ODE is linear. azy (i) i=0 = U (b) For the following second order ODE: + 2wn y + w / Y = u, y(0) = Yo, y(0) = Vo, express the Laplace transform result Y(s) in terms of yo, vo, and U(s). Write out the transfer function G(s) and find its poles and zeros for the following four conditions: $ = 0, & (0, 1), that wn > 0. = 1 and, 1. Note