Homework 5
1.
Problem 4.5 in the textbook.
Note that you found the ramp response you
need for this problem and the next one when you solved problem 4.4.
2.
Problem 4.7 in the textbook.
3.
Problem 4.9 in the textbook.
You might think about which form of the
convolution integral will be easiest to evaluate for this excitation.
4.
Problem 4.13 in the textbook.
Note that this is for an undamped system,
and that the “ramped step” example in the lecture is similar to this
problem.
Rather than using superposition of ramp responses as for
problem 4.7, set up and evaluate a convolution integral for the response in
each time interval (0 < t < T/2, T/2 < t < 3T/2, 3T/2 < t < 2T, t > 2T).
5.
Problem 4.16 in the textbook.
You might find Eqs. B.16, 18, and 19 in
Appendix B helpful.
6.
Problem 4.21 in the textbook.
The “shifting theorem” equations (Eqs. B.14
and 15) might be useful.
7.
Problem 5.8 in the textbook.
8.
Problem 5.16 in the textbook.
9.
Find the free vibration response of the system of Problems 5.8 and 5.16
with these initial conditions:
a.
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 Spring '10
 Staff
 Velocity, Diagonal matrix

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