Repeat Question 18 for the case where the displaced profile of the string is as shown in Figure 12.23.

Data from Question 18

A tightly stretched, flexible, uniform string has its ends fixed at the points x = 0 and x = l. The midpoint of the string is displaced a distance a, as shown in Figure 12.22. If f(x) denotes the displaced profile of the string, express f(x) as a Fourier series expansion consisting only of sine terms.

f(x) 4 14 - Figure 12.23 Displaced string 3/4 1 X