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A string is tied to the x-axis at x = 0 and at x = L and its initial displacement u(x, 0) = f(x), 0 < x < L, is shown in the given figure. Find u(x, t) if the string is released from rest. (Let a² = T/p, where Tis the magnitude of the tension in the string and p is the mass per unit length. Use a2 as the constant in the given boundary-value problem.) u(x, t) = 0 f(x) + h Need Help? Read It • 00 Σ( n=1 L13 8h sin ²n² ( 17 )cos ( 14 )sin (1x))) L x

A string is tied to the x-axis at x = 0 and at x = L and its initial displacement u(x, 0) = f(x), 0 < x < L, is shown in the given figure. Find u(x, t) if the string is released from rest. (Let a² = T/p, where Tis the magnitude of the tension in the string and p is the mass per unit length. Use a2 as the constant in the given boundary-value problem.) u(x, t) = 0 f(x) + h Need Help? Read It • 00 Σ( n=1 L13 8h sin ²n² ( 17 )cos ( 14 )sin (1x))) L x

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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A string is tied to the x-axis at x = 0 and at x = L and its initial displacement u(x, 0) = f(x), 0 < x < L, is shown in the given figure. Find u(x, t) if the string is released from rest. (Let a2 = T/p, where T is the magnitude of the tension in the string and p is the mass per unit length. Use a² as the constant in the given boundary-value problem.) u(x, t) = 0 f(x) 4 h Need Help? Read It 00 8h πη πη Σ( 3h (sin( 1 ) cos(™)sin ( + x)) 22 2 L πn² n = 1 L/3
Transcribed Image Text:A string is tied to the x-axis at x = 0 and at x = L and its initial displacement u(x, 0) = f(x), 0 < x < L, is shown in the given figure. Find u(x, t) if the string is released from rest. (Let a2 = T/p, where T is the magnitude of the tension in the string and p is the mass per unit length. Use a² as the constant in the given boundary-value problem.) u(x, t) = 0 f(x) 4 h Need Help? Read It 00 8h πη πη Σ( 3h (sin( 1 ) cos(™)sin ( + x)) 22 2 L πn² n = 1 L/3
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