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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. %3D u (0, t) = 0 =u (l, t) for all t. The initial deflection is %3D 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. %3D u (0, t) = 0 =u (l, t) for all t. The initial deflection is %3D 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 4 - 24 The string is fixed at the ends. u (0, t) 0 u (4, t) for all t. The initial deflection is %3D u (x. 0) = x; 0 <x < 1/2, u (4, 0) = 1-x; sxs ! 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 4 - 24 The string is fixed at the ends. u (0, t) 0 u (4, t) for all t. The initial deflection is %3D u (x. 0) = x; 0 <x < 1/2, u (4, 0) = 1-x; sxs ! and the initial velocity is zero. Find the deflection of the string at any instant of time.
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