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An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0sx<1, t> 0, at2 - əx² ' Where, u(x, t) is the displacement of the string. The initial conditions are given by ди (x, 0) = 0, 0

An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0sx<1, t> 0, at2 - əx² ' Where, u(x, t) is the displacement of the string. The initial conditions are given by ди (x, 0) = 0, 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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(b) An elastic string which is fixed at both ends is governed by the wave equation a?u a²u at2 Əx2 0<x< 1, t> 0, Where, u(x, t) is the displacement of the string. The initial conditions are given by 0<x< 0.5 Sx, u(x,0) = {-(x – 1) 0.5<x <1 ди at (x,0) = 0, 0< x<1 Determine the variation of the displacement of the string by using the finite- difference method for 0 < t < 0.3 s using Ax = 0.25 mm and At = 0.1 s.
Transcribed Image Text:(b) An elastic string which is fixed at both ends is governed by the wave equation a?u a²u at2 Əx2 0<x< 1, t> 0, Where, u(x, t) is the displacement of the string. The initial conditions are given by 0<x< 0.5 Sx, u(x,0) = {-(x – 1) 0.5<x <1 ди at (x,0) = 0, 0< x<1 Determine the variation of the displacement of the string by using the finite- difference method for 0 < t < 0.3 s using Ax = 0.25 mm and At = 0.1 s.
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