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 with 1- |æ|/2, for |x| < 2 $(x) = for |x| > 2 (i) Using d'Alembert's solution, give an explicit solution to this initial value problem.
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 with 1- |æ|/2, for |x| < 2 $(x) = for |x| > 2 (i) Using d'Alembert's solution, give an explicit solution to this initial value problem.
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Transcribed Image Text: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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