For the following function: i. Find an approximated expression for y ii. What is the effect of T_s and how it is related to the frequency of the sine wave iii. Use the backward shift operator and check the difference, compared to part (ii) iv. Compare the approximated results for y with its exact expression y(t) = sin(2t) + 1 dy(t)/dt = 2 cos(2t), y(0) = 1 dy(t)/dt = y(n + 1)T_s] – y[nT_s]/T_s = ?? y[(n + 1)T_s] = ?? For the following function: i. Solve for y_1 and y_2, as continuous systems, and prove that they are equal ii. Find an approximated expressions for y_1 and y_2 iii. Find an analytical expression for y = y_1 – y_2 and validate it via comparing it to both y_1 and y_2 iv. Find the maximum value of T_s to produce good results, in terms of accuracy. dy_1(t)/dt = 2(1 + 2e^-2t – y_1), y_1(0) = 3 dy_2(t)/dt = -8te^-2t, y_2(0) = 3 dy(t)/dt = y[(n + 1)T_s] – y[nT_s]/T_s = ?? y[(n + 1)T_s] = ??

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