See file for full description.
A string of length L is fixed at both ends. The speed of waves on the string is c. The string is initially displaced a distance h uniformly along its length, and is released from rest at t=0. (The string initially has a very large slope at x=0 and x=L; assume the slope is infinite.)
For w_n=ckn=cn*pi/L, the displacement of the string for t>=0 the displacement is
Sum(A_n*cos(wt) + B_n*sin(wt))© BrainMass Inc. brainmass.com October 24, 2018, 11:33 pm ad1c9bdddf
Hello and thank you for posting your question to Brainmass!
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
A string of length L is fixed at both ends. The speed of waves on the string is c. The string is initially ...
The attached file shows how to analyze a general solution of the wave equation using Fourier analysis.
Vibrating String and d'Alembert's Solution in Wave Equation
2. Show that, like the wave equation, the given PDE is hyperbolic and find its general solution by introducing the suggested change of variables.
(b) uxx - 4uxy - 5uyy = 0 ........
Please see the attached file for the fully formatted problems.