The solution of the wave equation Urx Gutt. 0 < r < 3. t > 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) uz(r, 0) = 2 sin () - 3 sin(2r2) + 2 sin(37z) is 0 and -- u(x, t) = E E sin () [an cos (2t) + b, sin (2t)] 2nnt COS where n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, b9 =+, b, = an = 0 otherwise Od ai an = bn O otherwise a6 4元) ag 2, a6 -3, ag =2, an O otherwise d) ai O e) None of these
The solution of the wave equation Urx Gutt. 0 < r < 3. t > 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial conditions u(x, 0) uz(r, 0) = 2 sin () - 3 sin(2r2) + 2 sin(37z) is 0 and -- u(x, t) = E E sin () [an cos (2t) + b, sin (2t)] 2nnt COS where n=1 O a) b1 = 2, b6 -3, bg = 2, bn O otherwise an O b) b1 = , , be = 7, b9 =+, b, = an = 0 otherwise Od ai an = bn O otherwise a6 4元) ag 2, a6 -3, ag =2, an O otherwise d) ai O e) None of these
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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Transcribed Image Text:The solution of the wave equation Urx
Gutt. 0 < x < 3. t > 0, which
satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial
conditions u(x, 0)
Ut(x, 0) = 2 sin() - 3 sin(2rx) + 2 sin(3rz) is
O and
--
2nnt.
u(x, t) = E sin () [an cos (2at) + b, sin
COS
3
where
3
n=1
O a) b1 = 2, b6
-3, bg = 2, bn
O otherwise
an
O b) b1 = ,
, be = 7, bg ==, b, = an = 0 otherwise
C a1
an = bn
O otherwise
a6
47
ag
-3, ag
2, an
0 otherwise
d) ai
2, a6
O e) None of these
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