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Consider a vibrating finite string with zero displacement at the ends Fu ₂0²u 01² ər² u(0, t) = 0, u(a, t) = 0 u(x,0) = 0, (PDE) (BC) (ICI) (IC2) ди Ət -(,0) = g(x) = A cos ={8 cnml a Find a Fourier series form for the solution u(r, t). Remark: You may use the fact that the product solutions of (PDE)-(BC) are of the form + B sin cn=l 00, a t> 0, 0

Consider a vibrating finite string with zero displacement at the ends Fu ₂0²u 01² ər² u(0, t) = 0, u(a, t) = 0 u(x,0) = 0, (PDE) (BC) (ICI) (IC2) ди Ət -(,0) = g(x) = A cos ={8 cnml a Find a Fourier series form for the solution u(r, t). Remark: You may use the fact that the product solutions of (PDE)-(BC) are of the form + B sin cn=l 00, a t> 0, 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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Consider a vibrating finite string with zero displacement at the ends Fu ₂²u (²5 01² ər² u(0, t) = 0, u(a, t) = 0 u(x,0) = 0, (PDE) (BC) (IC1) (IC2) ди Ət (1,0) = g(x) = cnml ={8 A cos- a Find a Fourier series form for the solution u(r, t). Remark: You may use the fact that the product solutions of (PDE)-(BC) are of the form + B sin cn=l 0<x<a,t>0, a t> 0, 0<x<a, 0≤x<a/3, a/3 ≤ x ≤a. sin NTI a where n is any positive integer, and A and B are arbitrary constants. You do not need to show the work of separation of variables.
Transcribed Image Text:Consider a vibrating finite string with zero displacement at the ends Fu ₂²u (²5 01² ər² u(0, t) = 0, u(a, t) = 0 u(x,0) = 0, (PDE) (BC) (IC1) (IC2) ди Ət (1,0) = g(x) = cnml ={8 A cos- a Find a Fourier series form for the solution u(r, t). Remark: You may use the fact that the product solutions of (PDE)-(BC) are of the form + B sin cn=l 0<x<a,t>0, a t> 0, 0<x<a, 0≤x<a/3, a/3 ≤ x ≤a. sin NTI a where n is any positive integer, and A and B are arbitrary constants. You do not need to show the work of separation of variables.
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