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).

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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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).

@
(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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