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The vibrations of an elastic string of length / are governed by the one-dimensional wave equation The string is fixed at the ends. u (0, t) = 0 = u (1, t) for all t. The initial deflection is u (x. 0) = x, 0

The vibrations of an elastic string of length / are governed by the one-dimensional wave equation The string is fixed at the ends. u (0, t) = 0 = u (1, t) for all t. The initial deflection is u (x. 0) = x, 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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The vibrations of an elastic string of length / are governed by the one-dimensional wave equation The string is fixed at the ends. u (0, t) = 0 = u (1, t) for all t. The initial deflection is u (a, 0) = 1-x; sx s! u (x. 0) = x, 0<x < 1/2, and the initial velocity is zero. Find the deflection of the string at any instant of time.
Transcribed Image Text:The vibrations of an elastic string of length / are governed by the one-dimensional wave equation The string is fixed at the ends. u (0, t) = 0 = u (1, t) for all t. The initial deflection is u (a, 0) = 1-x; sx s! u (x. 0) = x, 0<x < 1/2, and the initial velocity is zero. Find the deflection of the string at any instant of time.
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