Unformatted text preview: 2016 Fall Semester ME 501 Mechanical Engineering Analysis I Homework, Part 8: Fourier analysis Solutions 1. Find the Fourier series for the steady‐state oscillation given by the equation of motion (
1 and periodic : 2 and at 1
1 1 3 to Plot the energy spectrum of this oscillation in the range from . Solution: cos
4
For the mass‐spring problem: sin
1 1 1, 1, sin 1 1 Energy spectrum 1 2 3 4 5 6 7 8 9 10 10 0.927584529352185 0.003376818913804 0.000129951794002 0.000012946503561 0.000002167142723 0.000000503386527 0.000000146556059 0.000000050333614 0.000000019610734 0.000000008439774 1 /2: MATLAB code for calculation of the energy spectrum is in the source file HW8P2.m. 2. Find the steady‐state oscillation given by periodic : 2 and at 1
1 , where if if 0 0 Solution: sin
2 1 1 For the mass‐spring problem: sin 1, 1, sin 1
1
1 1 0 and 3. Calculate eigenvalues and eigenfunctions for the Sturm‐Liouville problem (set / 1 0, 1 0, Solution: sin log 0. ) ...
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 Spring '14
 WillardC.Schreiber

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