AA 242B: Mechanical Vibrations (Spring 2010)
Final
Due June 9, 2010
Problem 1
1. Explain why the system graphically depicted in Figure 1 simulates a “dam
aged” vehicle traveling on a rough road.
2. Compute the response
z
(
t
) as well as the force
f
(
t
) transmitted to the
vehicle. Would you buy such a car? Why?
Problem 2
1. Using an exact method, find the response of the system shown in Figure 2.
2. Using the added mass method, find the response of the same system.
3. Plot the timehistories of both computed responses and compare the ob
tained results.
Problem 3
Assume that
d
is such that the system shown in Figure 3 is lightly damped.
1. Compute a good approximation of each of its two damped
frequencies.
Problem 4
1. Find the eigenmodes of the discrete system shown in Figure 4.
2. Consider a freefree rod with a uniform cross section. Compute and plot
the first three natural modes of vibration of this rod.
3. Compare the answers to the above two questions and draw conclusions
concerning the analogy between discrete and continuous systems.
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 Spring '10
 CHARBELFARHAT
 Harmonic Series, Fundamental frequency, k2, Normal mode, Mode shape

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