a) [15 points] Let f(t) represents the output of an industrial system in time domain, and F(s) be its Laplace transform.

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A 15 Points Let F T Represents The Output Of An Industrial System In Time Domain And F S Be Its Laplace Transform 1 (141.27 KiB) Viewed 18 times

a) [15 points] Let f(t) represents the output of an industrial system in time domain, and F(s) be its Laplace transform. Find the Laplace Transform F(s). i) [5 points] f(t) = Acos(2t) - Be-7t + Cu(t), t≥0 ii) [10 points] f(t)=-7 t² u(t-D) Where A=-40, B=-13, C=75, D=6 b) [25 points] A manufacturing process is represented by the following block diagram: R(s) + K + H₂(s) G₁(s) H3(s) H₁(s) G₂(s) Y(s) i) [5 points] Do you need to apply Rule 1 and Rule 2 in the Lecture Notes to solve this question? Why / Why not? ii) [20 points] Simplify the block diagram to its most simplified form and find (Y(s))/(R(s)). Show each step in your solution. Where G₁(s) = 5s, G₂(s) = 3, K = 10, H₁(s) = 4, H₂(s) = 8 and H3(s) = 6s