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Find u(x, t) for the string of length L = 1 and c² = 16 when the initial velocity is zero and the initial deflection f(x) is as follows:

Find u(x, t) for the string of length L = 1 and c² = 16 when the initial velocity is zero and the initial deflection f(x) is as follows:

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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Find u(x, t) for the string of length L = 1 and c2 = 16 when the initial velocity is zero and the initial deflection f(x) is as follows: 1 1 1 1 1 1 1. и(х, t) — (V2-1)sin(πx) cos (4πί) +si-(2πx) σoS (8 πί) +y2 + 1)sin (3 π) cos (1 2π) + ... 1 1 (V2 - 1)sin(rx)cos(4rt)- si=(2rx)cos(8nt) + (/2 + 1)sin(3xx)cos(12rt) – 9. 2. и(х, t) %— ... 1 (V2. 1 (V2+ 1)sin(3ax)cos(12zt) + ... 1 3. и(х, t) — - 1)sin(πx)cos (4πί) + si= (2πx) cos (8 πί) + 1 4. и(х, t) — 1 :- 1 )sin(rx)cos(4nt) – si=(2x)cos(87t) +V2 + 1)sin(3x)cos(12rt) Choose the correct answer.
Transcribed Image Text:Find u(x, t) for the string of length L = 1 and c2 = 16 when the initial velocity is zero and the initial deflection f(x) is as follows: 1 1 1 1 1 1 1. и(х, t) — (V2-1)sin(πx) cos (4πί) +si-(2πx) σoS (8 πί) +y2 + 1)sin (3 π) cos (1 2π) + ... 1 1 (V2 - 1)sin(rx)cos(4rt)- si=(2rx)cos(8nt) + (/2 + 1)sin(3xx)cos(12rt) – 9. 2. и(х, t) %— ... 1 (V2. 1 (V2+ 1)sin(3ax)cos(12zt) + ... 1 3. и(х, t) — - 1)sin(πx)cos (4πί) + si= (2πx) cos (8 πί) + 1 4. и(х, t) — 1 :- 1 )sin(rx)cos(4nt) – si=(2x)cos(87t) +V2 + 1)sin(3x)cos(12rt) Choose the correct answer.
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