Consider the initial boundary value problem (IBVP) for the wave equation: a²u a²u 4 at2 0 0 (1) и(0, t) —D и(п, t) %3D 0, t > 0 (2) u(x,0) = 0,u¿(x, 0) = sin x ,0 < x < n (3) The series u(x, t) = E-[An cos(2nt) + B, sin(2nt)] sin(nx) satisfies the wave equation (1) and the boundary conditions (2). By using the initial conditions given in (3) determine the coefficients A, and B,, and then decide which of the following is the solution of the IBVP (1) – (3). A u(x, t) = sin 4t sin 2x В u(x,t) = cos 2t sin 2x COs u(x,t) = sin t sin x D u(x,t) = cos 2t sin x E u(x, t) = sin 2t sin x
Consider the initial boundary value problem (IBVP) for the wave equation: a²u a²u 4 at2 0 0 (1) и(0, t) —D и(п, t) %3D 0, t > 0 (2) u(x,0) = 0,u¿(x, 0) = sin x ,0 < x < n (3) The series u(x, t) = E-[An cos(2nt) + B, sin(2nt)] sin(nx) satisfies the wave equation (1) and the boundary conditions (2). By using the initial conditions given in (3) determine the coefficients A, and B,, and then decide which of the following is the solution of the IBVP (1) – (3). A u(x, t) = sin 4t sin 2x В u(x,t) = cos 2t sin 2x COs u(x,t) = sin t sin x D u(x,t) = cos 2t sin x E u(x, t) = sin 2t sin x
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
![Consider the initial boundary value problem (IBVP) for the wave equation:
a²u
a²u
4
at2
0 <x < T,
t > 0 (1)
и(0, t) —D и(п, t) %3D 0,
t > 0
(2)
u(x,0) = 0,u¿(x, 0) = sin x ,0 < x < n (3)
The series u(x, t) = E-[An cos(2nt) + B, sin(2nt)] sin(nx) satisfies the wave
equation (1) and the boundary conditions (2). By using the initial conditions given in (3)
determine the coefficients A, and B,, and then decide which of the following is the
solution of the IBVP (1) – (3).
A
u(x, t)
= sin 4t sin 2x
В
u(x,t) = cos 2t sin 2x
COs
u(x,t) = sin t sin x
D
u(x,t) = cos 2t sin x
E
u(x, t) = sin 2t sin x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda7726e0-a4d4-49c5-945c-a97b27f39831%2F3119df8b-990b-4935-820e-afc9a1f58dcf%2F8ub851_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial boundary value problem (IBVP) for the wave equation:
a²u
a²u
4
at2
0 <x < T,
t > 0 (1)
и(0, t) —D и(п, t) %3D 0,
t > 0
(2)
u(x,0) = 0,u¿(x, 0) = sin x ,0 < x < n (3)
The series u(x, t) = E-[An cos(2nt) + B, sin(2nt)] sin(nx) satisfies the wave
equation (1) and the boundary conditions (2). By using the initial conditions given in (3)
determine the coefficients A, and B,, and then decide which of the following is the
solution of the IBVP (1) – (3).
A
u(x, t)
= sin 4t sin 2x
В
u(x,t) = cos 2t sin 2x
COs
u(x,t) = sin t sin x
D
u(x,t) = cos 2t sin x
E
u(x, t) = sin 2t sin x
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
