HomeWork 1

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AE 617/AE 491 Structural Dynamics,
Homework –1
The problems are to be referred from ‘Elements of Vibration Analysis’ by Leonard
Meirovitch, second edition. Turn-in the homework sheets in my office R 131 on or
before 12-09-2014, 05:00 pm.
1. Problem No 1.12
2. Problem No 1.17
3. Problem No 1.25

4. Problem No 1.26

5. Problem No 1.28
6. Problem No 1.32
7. Appendix A of the text book mentions about the Fourier series. A different
periodic function is shown in Figure 1. Consider this f(t) ∀t and calculate the
response of a damped single degree of freedom system to this excitation. Plot
the (a) the function f(t) and superimpose sinusoids with 1 to 5 terms (b)the
solution x(t) for an accurate(5 terms or more) f(t).
0
f(t)
t
A
T/2 T/2 T/2 T/2
Figure 1: Signal
8. Example 2.6 in the text book shows the response of an undamped system
to an excitation of the form F(t) = F
0
sin λt U(t), where U(t) is unit step
function. Derive and plot the response of an underdamped system for the
same excitation. In another Figure, plot the above response along with a
response for F(t) = F
0
sin λt ∀t. Repeat this combined plot for different initial
conditions, (a) initially at rest, (b) x
0
= 0, ˙ x
0
̸= 0, (c) x
0
̸= 0, ˙ x
0
= 0, (d)
x
0
̸= 0, ˙ x
0
̸= 0. Give a detailed discussion of each case presented. You can
also plot the steady state solutions alone for both excitations in a single plot.

To determine the equilibrium positions and stability in these questions read section
1.4 in the textbook. (It is only optional to answer the sub-questions related to this
section)
1

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