ME 240
Introduction to Dynamics
Computer Assignment #2: Free and Forced Vibrations
The due dates are Thursday, 3/12
for Professor Karnopp's class and Friday 3/13 for Professor Grosh's class.
Problem Statement: In this assignment, Matlab is used to study
the effect of varying the stiffness, mass and damping factors for free
motion and the interaction of the drive frequency and the natural frequency
for forced vibration. The first two problems use information given here.
Problem 3 involves the complete (particular plus complimentary) solution
for the forced oscillator, this is part of problem 21-89.
System Parameters: For problems 1 and 2 in this assignment, the
values for the mass and stiffness are
m = 2 kg
k = 5000 N/m
c = you set the value for the 3 damping factors N sec/m
Change "c" to let the damping factor (zeta) take on values of 0.01,
0.1 and 0.9 for problems 1 and 2.
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Determine the free response for these three cases due to an initial
velocity of 1 m/s. Using Matlab plot the response (do not hand in).
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How does qualitative nature of the response change with the three damping
factors?
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Does the damped nautural frequency change noticeably?
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Use Matlab to plot the steady-state amplitude and phase for the same oscillator
system, varying the ratio of Omega/wn (drive frequency to natural frequency)
from 0 to 2.5. Draw the multiple plots for amplitude and phase angle on
the same page. Hand in the multiple plots (one page).
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NOW use the mass and stiffness to the values in problem 21-89. Plot the
total response (complimentary plus particular). Change the damping from
zeta = 0.379 to zeta = 0.0379 and replot. (Hand in both plots).
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What is the effect of damping on the amount of time taken to reach the
steady state response?
Step by Step Instructions:
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For problem (1).
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For Problem (2).
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For Problem (3)