Solve the wave equation using Fourier Transform: o'u ou - ∞ 0 %3D -12x utx, 0) = H(x)e u, (x, 0) = 0. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please short steps and final answer.
Solve the wave equation using Fourier Transform:
o'u ou
- c0 <x < 0, t>0
%3D
-12x
utx, 0) = H(x)e
%3D
u,(x, 0) = 0.
Oa.
u (x, t) = Real
sin wt
(12+iw)
%3D
2 я
Ob.
1
iwx
u (x,t) Real
cos wt
dw
(12+iw)
Oc.
iwx
u (x,1) Real
sın wt
%3D
w (12+iw)
Od.
1
u (x,1) = Real
cos wt
w (12+iw)
Oe
correct ancue
Transcribed Image Text:Please short steps and final answer. Solve the wave equation using Fourier Transform: o'u ou - c0 <x < 0, t>0 %3D -12x utx, 0) = H(x)e %3D u,(x, 0) = 0. Oa. u (x, t) = Real sin wt (12+iw) %3D 2 я Ob. 1 iwx u (x,t) Real cos wt dw (12+iw) Oc. iwx u (x,1) Real sın wt %3D w (12+iw) Od. 1 u (x,1) = Real cos wt w (12+iw) Oe correct ancue
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