Consider a system similar to that considered in Problem 1 but with a different transfer function:...

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Consider a system similar to that considered in Problem 1 but with a different transfer function: G(s) = 10 V(s) F(s) s+1 (2a) Let s = jo, find the magnitude |G(jw)| and the phase (@) of G(jw) =|G(jw)|e() as functions of frequency @ (rad/s). (4%). (2b) According to Corollary 2.31 (Page 5 of MEM255Lecture2B notes) or Corollary 2.33 (page 31 of the textbook), the steady-state sinusoidal response vs (t) due to the input f (t) = cos at u(t) should be V(t) = |G(jw) cos(@t + O(@)) Use this approach to find the steady-state sinusoidal response vs (t) due to the input f(t) = cost u(t). It should be in the form of v(t) = Acos(t+0). (4%). (2c) Let the initial condition and the input be v(0) = 0 and f(t) = cost u(t), respectively. Follow the procedure you learned from HW2 Problem 3c to find the complete solution v(t) of the system in the form of v(t) = v(t) +v (t) = A cos(t + 0) + Eet where 7 is the time constant of the system and E is a constant to be determined to satisfy the initial condition v(0) = 0. (4%). ss (2d) Use MATLAB plot to plot the transient response v(t), the steady-state response vs (t) the complete output response v(t) obtained in (2c) on a graph versus time t. On the same graph, please also plot the input function f(t) = cost so that you can compare the frequency, amplitude, and phase of the input and output. (4%). (2e) Use the graph obtained in (2d) to measure time constant of the transient response v, (t), and the amplitudes, periods, and the delay time between the input f(t) and the output v(t) at steady state. Then compare the oscillation frequency, the amplitude and the phase difference between the input f(t) = cost and output v(t) based on these measurements. (4%) Consider a system similar to that considered in Problem 1 but with a different transfer function: G(s) = 10 V(s) F(s) s+1 (2a) Let s = jo, find the magnitude |G(jw)| and the phase (@) of G(jw) =|G(jw)|e() as functions of frequency @ (rad/s). (4%). (2b) According to Corollary 2.31 (Page 5 of MEM255Lecture2B notes) or Corollary 2.33 (page 31 of the textbook), the steady-state sinusoidal response vs (t) due to the input f (t) = cos at u(t) should be V(t) = |G(jw) cos(@t + O(@)) Use this approach to find the steady-state sinusoidal response vs (t) due to the input f(t) = cost u(t). It should be in the form of v(t) = Acos(t+0). (4%). (2c) Let the initial condition and the input be v(0) = 0 and f(t) = cost u(t), respectively. Follow the procedure you learned from HW2 Problem 3c to find the complete solution v(t) of the system in the form of v(t) = v(t) +v (t) = A cos(t + 0) + Eet where 7 is the time constant of the system and E is a constant to be determined to satisfy the initial condition v(0) = 0. (4%). ss (2d) Use MATLAB plot to plot the transient response v(t), the steady-state response vs (t) the complete output response v(t) obtained in (2c) on a graph versus time t. On the same graph, please also plot the input function f(t) = cost so that you can compare the frequency, amplitude, and phase of the input and output. (4%). (2e) Use the graph obtained in (2d) to measure time constant of the transient response v, (t), and the amplitudes, periods, and the delay time between the input f(t) and the output v(t) at steady state. Then compare the oscillation frequency, the amplitude and the phase difference between the input f(t) = cost and output v(t) based on these measurements. (4%)