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(b) An elastic string which is fixed at both ends is governed by the wave equation ² ax² ² 0≤x≤ 1, t≥ 0, at² Where, u(x, t) is the displacement of the string. The initial conditions are given by u(x,0) = = {²(x - 1) -(x-1) 0≤x≤ 0.5 0.5 < x≤1 du 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.

(b) An elastic string which is fixed at both ends is governed by the wave equation ² ax² ² 0≤x≤ 1, t≥ 0, at² Where, u(x, t) is the displacement of the string. The initial conditions are given by u(x,0) = = {²(x - 1) -(x-1) 0≤x≤ 0.5 0.5 < x≤1 du 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.

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 a?u 0<x< 1, t> 0, atz Where, u(x, t) is the displacement of the string. The initial conditions are given by 0<x< 0.5 ди u(x,0) = {-(x – 1) Sx, l-(x – 1) 0.5 <x<1 (x,0) = 0, 0< x< 1 at 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 a?u 0<x< 1, t> 0, atz Where, u(x, t) is the displacement of the string. The initial conditions are given by 0<x< 0.5 ди u(x,0) = {-(x – 1) Sx, l-(x – 1) 0.5 <x<1 (x,0) = 0, 0< x< 1 at 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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