Consider the wave equation 16 u :0 for -o < x < o and t > 0 with boundary conditions (i) u(x, 0) = x*, and (ii) u (x, 0) = 0. Apply Fourier transforms to the wave equation with respect to a and let U(p, t) = F[u(x, t)]. Then the equation reduces to: O U (p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = 0 and B(p) = F[*]. %3| O (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = 0 and B(p) = F[a*]. %3D %3D O U(p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = Fa*] and B(p) = 0. %3D O U (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = F[x*] and B(p) = 0 none of these
Consider the wave equation 16 u :0 for -o < x < o and t > 0 with boundary conditions (i) u(x, 0) = x*, and (ii) u (x, 0) = 0. Apply Fourier transforms to the wave equation with respect to a and let U(p, t) = F[u(x, t)]. Then the equation reduces to: O U (p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = 0 and B(p) = F[*]. %3| O (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = 0 and B(p) = F[a*]. %3D %3D O U(p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = Fa*] and B(p) = 0. %3D O U (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = F[x*] and B(p) = 0 none of these
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![0 for -00 < x < 00 and t > 0 with
boundary conditions (i) u(x, 0) = x*, and (ii) u (x, 0) = 0. Apply Fourier transforms
to the wave equation with respect to a and let U(p, t) = F[u(x, t)]. Then the
Consider the wave equation
16 u
equation
reduces to:
O U (p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = 0 and B(p) = F[*].
%3|
O (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = 0 and B(p) = F[a*].
%3D
%3D
O U(p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = Fx*] and B(p) = 0.
%3D
O (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = F[x*] and B(p) = 0
none of these](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4181438-f87b-475d-bd8f-883e0f0c5958%2F277fc5d9-19c6-4671-9aea-98231bd9296b%2F8rb9ph_processed.jpeg&w=3840&q=75)
Transcribed Image Text:0 for -00 < x < 00 and t > 0 with
boundary conditions (i) u(x, 0) = x*, and (ii) u (x, 0) = 0. Apply Fourier transforms
to the wave equation with respect to a and let U(p, t) = F[u(x, t)]. Then the
Consider the wave equation
16 u
equation
reduces to:
O U (p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = 0 and B(p) = F[*].
%3|
O (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = 0 and B(p) = F[a*].
%3D
%3D
O U(p, t) = A(p) cos(4pt) + B(p) sin(4pt) where A(p) = Fx*] and B(p) = 0.
%3D
O (p, t) = A(p) cos(t) + B(p) sin(t) where A(p) = F[x*] and B(p) = 0
none of these
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