An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx² Where, u(x, t) is the displacement of the string. The initial conditions are given by
An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx² Where, u(x, t) is the displacement of the string. The initial conditions are given by
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Question
![(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,
əx?
Where, u(x, t) is the displacement of the string. The initial conditions are given by](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd47a654d-72f9-4035-8a3f-50b6731296e2%2F4ffeb38b-abeb-401e-a7b9-ef0c46a81cbb%2Ff2mffur_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 a?u
0 <x< 1, t> 0,
əx?
Where, u(x, t) is the displacement of the string. The initial conditions are given by
![0 < x< 0.5
u(x, 0) = {"x – 1)
(x,
l-(x – 1) 0.5 <x<1
ди
(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd47a654d-72f9-4035-8a3f-50b6731296e2%2F4ffeb38b-abeb-401e-a7b9-ef0c46a81cbb%2F7rqfsh4_processed.png&w=3840&q=75)
Transcribed Image Text:0 < x< 0.5
u(x, 0) = {"x – 1)
(x,
l-(x – 1) 0.5 <x<1
ди
(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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