b. An infinitely long string with zero initial displacement is subject to the initial velocity 0, if x < -1 10(x+1), if −1≤x≤0 10(1-x), if 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

could you do part b please

i. Show by direct substitution that
= H (x + at),
1/H(x+at),
2
where H is an arbitrary function, is a solution to the wave equation
a²uxx, aЄR, t≥0, -∞ < x <∞.
Utt -
u(x, t): = 1/2H(x-
H(x − at) +
ii. Explain concisely how the initial displacement, u(x, 0), will evolve over time?
You may include a plot if it helps your explanation.
b. An infinitely long string with zero initial displacement is subject to the initial velocity
0,
if x < -1
10(x+1), if −1≤ x ≤ 0
10(1-x), if 0<x<1
if 1 < x.
(x) =
0,
If the wave speed is c = = 1, find the displacement of the string, u(x, t), at subsequent
times.
Transcribed Image Text:i. Show by direct substitution that = H (x + at), 1/H(x+at), 2 where H is an arbitrary function, is a solution to the wave equation a²uxx, aЄR, t≥0, -∞ < x <∞. Utt - u(x, t): = 1/2H(x- H(x − at) + ii. Explain concisely how the initial displacement, u(x, 0), will evolve over time? You may include a plot if it helps your explanation. b. An infinitely long string with zero initial displacement is subject to the initial velocity 0, if x < -1 10(x+1), if −1≤ x ≤ 0 10(1-x), if 0<x<1 if 1 < x. (x) = 0, If the wave speed is c = = 1, find the displacement of the string, u(x, t), at subsequent times.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,