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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 26E
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Question
![(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4767c10-d626-4830-9068-4518cd16076d%2F0b2e95bc-1b6f-4139-928e-d94ffbc5a982%2Fto6ymm_processed.png&w=3840&q=75)
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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