Fall 1998, METBD 451 - FEA Dynamic Applications

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

Homework Assignment 1

from "Mechanical Vibrations" by J.P. DenHartog, Dover, 1985, Example on Vector Addition, Page 5.

Find the maximum amplitude of the sum of these two motions:

X1 = 5 sin 25t in.

X2 = 10 sin (25t + 1) in.

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

Addition is proper since both vibrations have the same frequency, omega = 25 rad/sec.

The period, T = 2(pi)/(omega) = 0.25132 sec/cycle

• Using a spreadsheet program, evaluate the functions (in small steps) over one cycle.
        (List Time vs. X1, X2, R).
• Graph all three results (X1, X2, and R). Mark the maximum amplitude of the resultant, R.    (Fully label and format your graph).

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  Homework Assignment 2

  Mechanical Vibrations, Motion Addition

  Find the maximum amplitude of the sum of these two motions over 1.0 second (combine by superposition):

  X1 = 5 sin 25t in.

  X2 = 10 sin (35t + 1) in.

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

  Frequency-1, (omega)1 = 25 rad/sec.    Period, T1 = 2(pi)/(omega) = 0.25132 sec/cycle

  Frequency-2, (omega)2 = 35 rad/sec.    Period, T2 = 2(pi)/(omega) = 0.17951 sec/cycle

• Using a spreadsheet program, evaluate the functions (in small steps) over 1 second.
        (List Time vs. X1, X2, R).
• Graph all three results (X1, X2, and R). Mark the maximum and minimum amplitude of R.    (Fully label and format your graph).

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