#2 Need A and B Consider a vibrating semi-infinite string over 0 < 0,u(0, t) = 0t> 0,u(r, t) remains bounded as → ∞Iu(x,0) = f(x) =диƏt-(x,0) = 04-x0t> 0,0≤x<∞.0≤x≤ 2,(IC2)(a) Sketch the graph of f(r) vs I.(b) Sketch the graph of u(r, t) vs r for time t = 1, using d'Alembert's solution formula.2 ≤ x < 4,4≤0<∞,

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Answered: Consider a vibrating semi-infinite…

Consider a vibrating semi-infinite string over 0 < 0, u(r. t) remains bounded as r→ ∞ I u(x,0) = f(x) = ди Ət 0 0, -(x,0) = 0 4-x 0 0NIVX. t> 0, 0≤x≤ 2, 2 ≤ x < 4, 4≤0

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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Question

#2
Need A and B

Consider a vibrating semi-infinite string over 0 <<x, with zero displace
ment at the left end:
(PDE)
(BC1)
(BC2)
(IC1)
J²u Ju
2+2 ər²
0<x<∞,t> 0,
u(0, t) = 0
t> 0,
u(r, t) remains bounded as → ∞
I
u(x,0) = f(x) =
ди
Ət
-(x,0) = 0
4-x
0
t> 0,
0≤x<∞.
0≤x≤ 2,
(IC2)
(a) Sketch the graph of f(r) vs I.
(b) Sketch the graph of u(r, t) vs r for time t = 1, using d'Alembert's solution formula.
2 ≤ x < 4,
4≤0<∞,

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