I need your help. 1. The following data represent the vibration amplitude in mm

Question

I need your help.

1. The following data represent the vibration amplitude in mm at a location on a helicopter fuselage panel during one-half rotation of the (two-bladed) rotor y 3.5 6.0 9.0 11.7 14.1 15.3 8.5 8.0 9.1 10-1 10.9 8.6 1.05 -1.9 -3.2 -4.7 -4.8 -3.9 -1.7 0.5 (a Find the real discrete Fourier transform for this data set (b) Any term in the Fourier series can be written: ck cos(kuut ok) where ck ale and E tan. Find the ck's (including co and plot their amplitude on a bar graph vs. k to illustrate the relative size of each term in the series. Explain the significance of the plot (c) Plot the function. inverse Fourier transform and the original data on the same plot. would you feel comfortable using this function to interpolate the data? Why or why not (d) Estimate the maximum velocity amplitude at this location on the fuselage panel.

Explanation / Answer

Given Values:

Real DIscrete Fourier Transform Result :

1 3.5 2 6 3 9 4 11.7 5 14.1 6 15.3 7 8.5 8 8 9 9.1 10 10.1 11 10.9 12 8.6 13 1.05 14 -1.9 15 -3.2 16 -4.7 17 -4.8 18 -3.9 19 -1.7 20 0.5

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