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4. (a) A finite string of length has the left end fixed and the right end free. The ㅠ initial displacement is zero, and the initial velocity is given by the function (x) = sin (). Find the vibrations of the string for t > 0, 0≤x≤n; that is, solve =a²uzz TER Uμ = u (t,0)=u, (t, x) = 0 (2) u (0, x) = 0, u, (0, 2) = sin( (b) Now assume that the string is infinite with the same initial conditions. Solve the problem using d'Alembert's formula.

4. (a) A finite string of length has the left end fixed and the right end free. The ㅠ initial displacement is zero, and the initial velocity is given by the function (x) = sin (). Find the vibrations of the string for t > 0, 0≤x≤n; that is, solve =a²uzz TER Uμ = u (t,0)=u, (t, x) = 0 (2) u (0, x) = 0, u, (0, 2) = sin( (b) Now assume that the string is infinite with the same initial conditions. Solve the problem using d'Alembert's formula.

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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4. (a) A finite string of length 7 has the left end fixed and the right end free. The initial displacement is zero, and the initial velocity is given by the function (x) = sin (). Find the vibrations of the string for t > 0, 0≤x≤; that is, solve uμ = a²u₂ IER u (t,0)=u, (t, x) = 0 u (0, x) = 0, u, (0, x) = sin 3x (b) Now assume that the string is infinite with the same initial conditions. Solve the problem using d'Alembert's formula.
Transcribed Image Text:4. (a) A finite string of length 7 has the left end fixed and the right end free. The initial displacement is zero, and the initial velocity is given by the function (x) = sin (). Find the vibrations of the string for t > 0, 0≤x≤; that is, solve uμ = a²u₂ IER u (t,0)=u, (t, x) = 0 u (0, x) = 0, u, (0, x) = sin 3x (b) Now assume that the string is infinite with the same initial conditions. Solve the problem using d'Alembert's formula.
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