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Assume a displacement sensor can be represented as a first-order system as follows dy(t) T + y(t) = bx(t) dt where x(t) represents displacement (mm), and y(t) represents the output (V). Assume all initial conditions are zero. = a. Assume b 3. Calculate and plot from time t = 0 to t 30 seconds every 0.2 seconds the response to a unit step increase in displacement when t = 1 and T = 5. Discuss the role of t in the system's response and in determining the time constant. b. Let x(t) = 1.0sin(2π0.1t). Calculate and plot the response to x(t) when t = 1 and t = 5. Plot both the input x(t) and the output y(t) on the same panel. Discuss the role of t in the system's response.
One could argue that a better representation of the displacement sensor is given by: d²y(t) dy(t) ·+63· +9y(t) = 9x(t) dt² dt a. Find and plot the response of the system above to a unit step increase in displacement when = 0.3 and when = 0.707. b. Let x(t) = 1.0 sin(2π0.1t). Calculate and plot the response to x(t) when 3 = 0.3 and when <= 0.707. Discuss the apparent role of 3 in the system's response. Let the input x (t) be the data in file "HWI_Q2.dat". Calculate and plot the response to x(t) (data from file) when 3 = 0.3 and when 3 = 0.707. Calculate the mean squared error between the input and the output for both values of 3. Discuss the apparent role of 3 in the system's response. C.