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a) Consider the function u(x, t) that is govern by the wave equation: 1 a2u with c = 3 c2 at2 subject to the following conditions. At x = 0 and x = 3, u = 0 for all t 2 0 and for 0 . (Ancos 3 + Brsin- sin n=1

a) Consider the function u(x, t) that is govern by the wave equation: 1 a2u with c = 3 c2 at2 subject to the following conditions. At x = 0 and x = 3, u = 0 for all t 2 0 and for 0 . (Ancos 3 + Brsin- sin n=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Consider the function u(x, t) that is govern by the wave equation: 1 a²u %3D with c = 3 Əx? c2 at² subject to the following conditions. At x = 0 and x = 3, u = 0 for all t > 0 and for 0 <x< 3. Using the method of separation of variables and applying the boundary conditions establish that the solution for u(x, t) may be written as: 2пnt 2пnt Un (x, t) = >. NITX sin 3 (Ancos 3 + Brsin- n=1
Transcribed Image Text:a) Consider the function u(x, t) that is govern by the wave equation: 1 a²u %3D with c = 3 Əx? c2 at² subject to the following conditions. At x = 0 and x = 3, u = 0 for all t > 0 and for 0 <x< 3. Using the method of separation of variables and applying the boundary conditions establish that the solution for u(x, t) may be written as: 2пnt 2пnt Un (x, t) = >. NITX sin 3 (Ancos 3 + Brsin- n=1
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