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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

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
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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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<∞,
Transcribed Image Text: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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