the end points: Consider a vibrating finite string over 0≤x≤6, with zero displacemen (PDE) (BC) (IC1) (IC2) J²u J²u Ət² əx² u(0, t) = 0, u(6, t) = 0 u(x,0) = f(x) = { 12 du at (,0) = 0 0 0, t> 0, 12 - 2x 0≤x≤ 6. 0≤x≤ 4, 4≤ x ≤ 6, (a) Sketch the graph of f(z) vs I. (b) Sketch the graph of u(x, t) vs z for time t = 1, using d'Alembert's solution formula

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Need A and B

Both graphs

the end points:
Consider a vibrating finite string over 0≤x≤6, with zero displacemen
J²u J²u
Ət²
əx²
u(0, t) = 0, u(6, t) = 0
u(x,0) = f(x) = {
{12-2x
ди
-(x,0) = 0
0≤x≤ 6.
Ət
(PDE)
(BC)
(IC1)
(IC2)
(a) Sketch the graph of f(x) vs I.
(b) Sketch the graph of u(x, t) vs z for time t = 1, using d'Alembert's solution formula.
0<x<6,t> 0,
t> 0,
0≤x≤ 4,
4≤ x ≤ 6,
Transcribed Image Text:the end points: Consider a vibrating finite string over 0≤x≤6, with zero displacemen J²u J²u Ət² əx² u(0, t) = 0, u(6, t) = 0 u(x,0) = f(x) = { {12-2x ди -(x,0) = 0 0≤x≤ 6. Ət (PDE) (BC) (IC1) (IC2) (a) Sketch the graph of f(x) vs I. (b) Sketch the graph of u(x, t) vs z for time t = 1, using d'Alembert's solution formula. 0<x<6,t> 0, t> 0, 0≤x≤ 4, 4≤ x ≤ 6,
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