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(1) (10%) If r(t) = 2cos (t + θ) and y(t) = Acos (t + 45°), obtain values of Oand A.

(2) (20%) Given a unit step input, it is known that. Determine y(t) using the inverse Laplace transform approach without solving differential equations.

(1) (10%) The control objective is 2% settling time of the dominant poles needs to be 4 sec. Find the value of K to meet this requirement.

(2) (10%) The control objective is damping ratio of the dominate poles is equal to 0.707. Dosign the value of K in order to reach this goal.

3.(26%) With r(t) as the input and y() as the output, this problem considers a linear system that can be represented by  where R(s) and Y(s) are the Laplace transforms of r(V) and y(t), respectively. With r(t) = cos21, it is known that the steady-state response of this system can be represented as Acos(at - π). Based on such information, please determine A, d, and T.

4.(24%) This problem considers six transfer functions G1 = 1/(s+1), G2 = 2/(s+2), G3 = 1/(s2+s+1),G4 = 3(s2+s+3), G5 =2/(s2+3s+2), and G6 = (s+10)((s2+s+10). Their step responses (AI, A2 , A6) are amplitude spectra (B1, B2 , B6) are given in the figures shown in the following pages. Please pair each of the transfer functions to one of the step responses and one of the amplitude spectra.(That is, if you think A1 is the step response of G1 and B1 is the amplitude spectrum of GI, write your answer for G1 as G1-A1-B1. Please present your answers in this way for all the six transfer functions considered in this problem.

(1)請解釋:何謂「在地老化」(aging inplace)?「活躍老化」(activeaging)?

(2)請你以在地老化」、「活躍老化」的概念,針對:農村「高齡者生活改善工 作」,提出三項重要的工作重點。

2.有關家政推廣(1)你認為「家政推廣員」的重要角色為何？請列舉三個重要角色。

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