Given the wave equation on an infinite string. Use the D′Alembert formula to calculate the solution y(x, t) y that satisfies the following initial conditions (see image): In each case draw the motion of the string according to your solution for t = 0, 1/2, 1, 3/2 [s] (Draw the transverse displacement profiles of the chord. For simplicity, you can assume c = 1).
Given the wave equation on an infinite string. Use the D′Alembert formula to calculate the solution y(x, t) y that satisfies the following initial conditions (see image): In each case draw the motion of the string according to your solution for t = 0, 1/2, 1, 3/2 [s] (Draw the transverse displacement profiles of the chord. For simplicity, you can assume c = 1).
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 4ST
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Question
Given the wave equation on an infinite string. Use the D′Alembert formula to calculate the
solution y(x, t) y that satisfies the following initial conditions (see image):
In each case draw the motion of the string according to your solution for t = 0, 1/2, 1, 3/2 [s] (Draw the transverse displacement profiles of the chord. For simplicity, you can assume c = 1).
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(b)
−1≤ x ≤0
x+1
y(x, 0) = f(x) =
1-2x 0≤x≤
0
otherwise
y(x,0) = f(x) = 0
dy
Ət It=0
=
g(x) =
=
dy
Ət It=0
−1 −1≤x≤<0
0≤x≤ 1/1/2
0
otherwise
=
= g(x) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd3e8a18-468c-4628-a56b-6591b35fa38f%2Face3a2d6-dd9e-4b4d-b542-06f3fe6cea1b%2Fpss7vm_processed.png&w=3840&q=75)
Transcribed Image Text:@
(b)
−1≤ x ≤0
x+1
y(x, 0) = f(x) =
1-2x 0≤x≤
0
otherwise
y(x,0) = f(x) = 0
dy
Ət It=0
=
g(x) =
=
dy
Ət It=0
−1 −1≤x≤<0
0≤x≤ 1/1/2
0
otherwise
=
= g(x) = 0
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