(c) Consider the system described by the same differential equation 0.5y(t) + y(t) = 2u(t), but...

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(c) Consider the system described by the same differential equation 0.5y(t) + y(t) = 2u(t), but the input is NOT necessarily a unit step function. Let U(s) and Y(s) be the Laplace transform of u(t) and y(t), respectively. Then the input/output relationship of the system can be described by the algebraic equation: Y(s) = G(s)U(s), where G(s) is called the transfer function. Find the transfer function G (s). (20%) (d) Let G(j2) = Aeo, Compute the magnitude A and the phase 0. (20%) (e) Let y(0) = 0 and u(t)= cos 2t, when t0. Find y (t), the output of the system at steady state using the approach described in Corollary 2.33. (20%) (c) Consider the system described by the same differential equation 0.5y(t) + y(t) = 2u(t), but the input is NOT necessarily a unit step function. Let U(s) and Y(s) be the Laplace transform of u(t) and y(t), respectively. Then the input/output relationship of the system can be described by the algebraic equation: Y(s) = G(s)U(s), where G(s) is called the transfer function. Find the transfer function G (s). (20%) (d) Let G(j2) = Aeo, Compute the magnitude A and the phase 0. (20%) (e) Let y(0) = 0 and u(t)= cos 2t, when t0. Find y (t), the output of the system at steady state using the approach described in Corollary 2.33. (20%)

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Based on the information from the image you have a system described by a differential equation and you are asked to work with the Laplace transform to ... View the full answer