The two-dimensional wave equation describing the vibrations of an infi- nite string is Θη Ot2 2021 მ2 where n = n(x,t), — -x< x < ∞ and c > 0 is a constant. Its general solution can be written as n(x,t) = F(x-ct) + G(x + ct), with F and G arbitrary smooth functions. If at time t = 0 the shape of the string is n(x, t = 0) at 9 = 5+x4 and the string is released with velocity (x, t = 0) = 0, determine n(x,t) for t > 0.

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The two-dimensional wave equation describing the vibrations of an infi-
nite string is
Θη
Ot2
2021
მ2
where n = n(x,t), —
-x< x < ∞ and c > 0 is a constant. Its general
solution can be written as
n(x,t) = F(x-ct) + G(x + ct),
with F and G arbitrary smooth functions. If at time t = 0 the shape of
the string is n(x, t = 0)
at
9
=
5+x4
and the string is released with velocity
(x, t = 0) = 0, determine n(x,t) for t > 0.
Transcribed Image Text:The two-dimensional wave equation describing the vibrations of an infi- nite string is Θη Ot2 2021 მ2 where n = n(x,t), — -x< x < ∞ and c > 0 is a constant. Its general solution can be written as n(x,t) = F(x-ct) + G(x + ct), with F and G arbitrary smooth functions. If at time t = 0 the shape of the string is n(x, t = 0) at 9 = 5+x4 and the string is released with velocity (x, t = 0) = 0, determine n(x,t) for t > 0.
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