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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
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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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
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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