Semi- Infinite String: consider the following wave equation describing the semi-infinite vibrating string problem Pu х> 0, t > 0, = dx²' u(x, 0) = f(x), x > 0 ди - (х, 0) 3D g(x), х>0 dt ди (0, t) = 0, t> 0 dx a) Find the d'Alembert's solution to the initial/boundary value problem. [Assuming that u is continuous at x = 0, t = 0.]
Semi- Infinite String: consider the following wave equation describing the semi-infinite vibrating string problem Pu х> 0, t > 0, = dx²' u(x, 0) = f(x), x > 0 ди - (х, 0) 3D g(x), х>0 dt ди (0, t) = 0, t> 0 dx a) Find the d'Alembert's solution to the initial/boundary value problem. [Assuming that u is continuous at x = 0, 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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![Semi- Infinite String: consider the following wave equation
describing the semi-infinite vibrating string problem
х> 0, t> 0,
dx2
u(x,0) = f(x),
x > 0
ди
(x, 0) = g(x), x > 0
dt
ди
(0, t) = 0,
t > 0
dx
a) Find the d'Alembert's solution to the initial/boundary value
problem. [Assuming that u is continuous at x = 0, t = 0.]
b) Show that the solution found in part (a) maybe obtained by
extending the initial position and velocity as even functions
(around x = 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e69957f-abc4-42a5-ae54-6067c6a171e5%2F49207c3b-5f74-4b57-90a0-331751e7ef2a%2Foasesed_processed.png&w=3840&q=75)
Transcribed Image Text:Semi- Infinite String: consider the following wave equation
describing the semi-infinite vibrating string problem
х> 0, t> 0,
dx2
u(x,0) = f(x),
x > 0
ди
(x, 0) = g(x), x > 0
dt
ди
(0, t) = 0,
t > 0
dx
a) Find the d'Alembert's solution to the initial/boundary value
problem. [Assuming that u is continuous at x = 0, t = 0.]
b) Show that the solution found in part (a) maybe obtained by
extending the initial position and velocity as even functions
(around x = 0).
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