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An infinite horizontal string is plucked. The vertical displacement of the string is the solution
to the following initial value problem
x E R, t > 0
u(x,0) = ¢(x)
ди
(x, 0) = 0
Ət
with
[- |x|/2, for x|< 2
O(x) =
0,
for |x| > 2
(i) Using d'Alembert's solution, give an explicit solution to this initial value problem.

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