
8.11. Plot the solution y(x, t) of Equation 8.30 using a one-term (η
1
Y
1
), a two-term (η
1
Y
1
+ η
2
Y
2
), and
a three-term (η
1
Y
1
+ η
2
Y
2
+η
3
Y
3
) approximation. What conclusions can be drawn?
Solution: Figure 34 shows the response at the free end using one, two and three term approximations. There
is almost no difference between the two and three term approximations, and the two term approximation
can yield fairly accurate results.
Figure 34: One, two, and three term approximation to the response y (L, t) for Problem 10.
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