Given a problem of the time dependent forced vibrations of the finite string as follows: V Length of the string is equal 5, tension is 200 and density is equal 4. V Displacement of the left hand end depends on time and equal of the string it is given a force equal sint. t2 and on the right hand end 7nx V Initial displacement of the string is equal -3sin- 17nx + 8sin· 10 2 V The string is exited with the Initial velocity equal 6sin x2 3nx + 2 V The force acting to the string is expressed by the function x2 4t . 10 2(x – 5)2 21πχ -10 sint – 10t sin- 2 sin t + 25 Your task followings: 1. Specify the problem as mathematical model. Problem for u(x,t). 2. Write appropriate Transformation v(x, t) for the Step 1. 3. Finalize Step 1 and specify the problem for v(x, t). 4. Find v(x, t). 5. Find the solution of the problem u(x, t). 6. Draw the graph u(x, 10) which is the displacement at the time t = 10. 7. Draw the graph u(1, t) which is the displacement of the point x = 1 in the time interval 0 < t< 10.
Given a problem of the time dependent forced vibrations of the finite string as follows: V Length of the string is equal 5, tension is 200 and density is equal 4. V Displacement of the left hand end depends on time and equal of the string it is given a force equal sint. t2 and on the right hand end 7nx V Initial displacement of the string is equal -3sin- 17nx + 8sin· 10 2 V The string is exited with the Initial velocity equal 6sin x2 3nx + 2 V The force acting to the string is expressed by the function x2 4t . 10 2(x – 5)2 21πχ -10 sint – 10t sin- 2 sin t + 25 Your task followings: 1. Specify the problem as mathematical model. Problem for u(x,t). 2. Write appropriate Transformation v(x, t) for the Step 1. 3. Finalize Step 1 and specify the problem for v(x, t). 4. Find v(x, t). 5. Find the solution of the problem u(x, t). 6. Draw the graph u(x, 10) which is the displacement at the time t = 10. 7. Draw the graph u(1, t) which is the displacement of the point x = 1 in the time interval 0 < t< 10.
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
100%
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 6 images
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,