Please help with questions C through F

6.25s3 3750s2 + 750,000s 50,000,000 5056 + 12555 + 25,088s4 + 30,01 1st + 3,004,000s2 + 750,000s + 50,000,000 H (s) + (a) Assuming the input to the system, U(t) is a step with magnitude, Uo. Use the Final Value Theorem to compute the final value of the system response. What does this say about the system response? (b) What is the dcgain of this system? How does this tie to the answer you got in (a)? Does it make sense (c) Use the MATLAB command 'pfract to determine the modes of the system. What are the time constants, damping ratios, and frequencies of the different modes? Write down the commands you used in MATLAB to get all of the answers. (d) Enter each mode as a separate transfer function into MATLAB, H1(s), H2(s), and H3(s). Use the impulse' command to compare the impulse response of all of the modes as well as to the total response, H(s). Limit the time interval to 5 seconds. Write down the commands that you used in MATLAB to get the plots. Attach the plot to your homework. Make sure the plot shows each curve distinctly from the others and that the legend identifies each curve. (e) Which mode most closely resembles the total system response? Why? (f) Approximate the system response using only the dominant mode. What DCgain value did you use? In MATLAB, plot the approximate solution you came up with and the total system response, H(s). How close did you get? Do you think that this is a good approximation? Attach the plot to your homework. Make sure the plot shows each curve distinctly from the other and that the legend identifies each curve