The free symmetric аги 1ди 1 др2 r dr + =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
M!44
Transcribed Image Text:the equation
with
The free symmetric vibrations of a very large membrane are governed by
a²u
дрг
+
Show that, for t > 0,
lau 1 J²U
r ər - c² Ət²
r> 0; t > 0
au
U = f(r), Ət g(r), when t = 0
1
U(r, t) = { pF(p) cos (pct) Jo(pr) dp +
G(p) sin (pct) Jo(pr) dp,
C
where F(p) and G(p) are the zero order Hankel transforms of f(r), g(r) respectively.
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