Fall 1998, METBD 451 - FEA Dynamic Applications

Prof. Dave Johnson, dhj1@psu.edu, Penn State - Erie, The Behrend College

Homework Assignment 4

from "Mechanical Vibrations" by J.P. DenHartog, Dover, 1985,
Exercise on Harmonic Beats, Page 5.

Find the displacement of the sum of these two motions:

X1 = 3 sin 40t in.

X2 = 4 sin 41t in.

(i.e., find R = X1 + X2)

• Using a spreadsheet program, evaluate the functions (in small steps) over four seconds.
        (Columns of Time vs. X1, X2, R).
• Graph all three results (X1, X2, and R). Graph the resultant, R, seperately.    (Fully label and format your graph).

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  Homework Assignment 5

  from "Mechanical Vibrations" by J.P. DenHartog, Dover, 1985,
  Non-Harmonic Periodic Motions, Fourier Series, Page 17.

  Use a Fourier series to approximate a square wave.
  Evaluate the Fourier equation on Page 19 with Fo = 5 lb.

• Using a spreadsheet program, evaluate the function (in small steps) over 20 radians,
        i.e. from (omega)t = 0 up to (omega)t = 20
        You must decide how many terms of the Fourier series are required
        to make a fair approximation of the square wave shape.
• Graph your square wave approximation.  (Fully label and format your graph).
• On the graph, note the number of Fourier series terms you chose to use.

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