2. u(0,t)=02. Consider a piano string of length L=Utt50cm that satisfies the wave equation-= 81uxx, 0 < x < 50, t> 0Assume that the ends of the string are fixed and the string is set in motion (i.e. struck by a hammer)from a resting position with an initial velocityut (x,0) = g(x) =Find the displacement u(x, t) of the string.4x,0≤x≤ 25200 4x, 25 < x < 50u(50,t)=0

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Answered: u(0,t)=0 2. Consider a piano string of…

u(0,t)=0 2. Consider a piano string of length L = 50cm that satisfies the wave equation Utt81Uxx, 0 0 4x, 2004x, 0≤x≤ 25 25 < x < 50 u(50,t)=0

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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Question

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u(0,t)=0
2. Consider a piano string of length L
=
Utt
50cm that satisfies the wave equation
-
= 81uxx, 0 < x < 50, t> 0
Assume that the ends of the string are fixed and the string is set in motion (i.e. struck by a hammer)
from a resting position with an initial velocity
ut (x,0) = g(x) =
Find the displacement u(x, t) of the string.
4x,
0≤x≤ 25
200 4x, 25 < x < 50
u(50,t)=0

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