4. (a) A finite string of length 7 has the left end fixed and the right end free. Theinitial 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≤; thatis, solveuμ = a²u₂ IERu (t,0)=u, (t, x) = 0u (0, x) = 0, u, (0, x) = sin3x(b) Now assume that the string is infinite with the same initial conditions. Solvethe 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.

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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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