Q1) Solve the wave equation of the circular membrane of radius 4 assuming the axisymmetry subjected to the following conditions u(r,0) = u(4,t) =0, t>0 and u,(r,0)=1. Q2) Solve the wave equation u It " = u 00 XX subject to u(0,t) = u(2,t) =0, t>0 and u(x,0)=0, u(x,0)= sin (3лx), 00, " 18 " 00 with u¸ (0,t) = . X |u(x, 0) = { 1, 0
Q1) Solve the wave equation of the circular membrane of radius 4 assuming the axisymmetry subjected to the following conditions u(r,0) = u(4,t) =0, t>0 and u,(r,0)=1. Q2) Solve the wave equation u It " = u 00 XX subject to u(0,t) = u(2,t) =0, t>0 and u(x,0)=0, u(x,0)= sin (3лx), 00, " 18 " 00 with u¸ (0,t) = . X |u(x, 0) = { 1, 0
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
![Q1) Solve the wave equation of the circular membrane of radius 4 assuming the axisymmetry
subjected to the following conditions
u(r,0) = u(4,t) =0, t>0 and u,(r,0)=1.
Q2) Solve the wave equation u
It
"
= u 0<x<2, t>0
XX
subject to u(0,t) = u(2,t) =0, t>0 and
u(x,0)=0, u(x,0)= sin (3лx), 0<x<2.
Find the exact value of u
1 1
18
Q3) Solve the heat equation u=u
t
= u(x,t) =0, t>0,
"
18
"
0<x<л, t>0 with
u¸ (0,t) = .
X
|u(x, 0) = {
1, 0<x<
元
0, 5<<x
-
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feed1351b-686f-4d8e-80ba-a8bc3ffcf56d%2Fb5f0f10f-6a30-409c-82c4-1007c96ee1c6%2Fh6mhh2f_processed.png&w=3840&q=75)
Transcribed Image Text:Q1) Solve the wave equation of the circular membrane of radius 4 assuming the axisymmetry
subjected to the following conditions
u(r,0) = u(4,t) =0, t>0 and u,(r,0)=1.
Q2) Solve the wave equation u
It
"
= u 0<x<2, t>0
XX
subject to u(0,t) = u(2,t) =0, t>0 and
u(x,0)=0, u(x,0)= sin (3лx), 0<x<2.
Find the exact value of u
1 1
18
Q3) Solve the heat equation u=u
t
= u(x,t) =0, t>0,
"
18
"
0<x<л, t>0 with
u¸ (0,t) = .
X
|u(x, 0) = {
1, 0<x<
元
0, 5<<x
-
2
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