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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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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 t? and on the right hand end of the string it is given a force equal sint. V Initial displacement of the string is equal -3sin* + 8sin 17nx 10 2 3nx V The string is exited with the Initial velocity equal 6sin v The force acting to the string is expressed by the function 10 x2 sin t + 10 2(х — 5)2 21πχ -10 sint – 10t sin- 2 - 4t2 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.
Transcribed Image Text: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 t? and on the right hand end of the string it is given a force equal sint. V Initial displacement of the string is equal -3sin* + 8sin 17nx 10 2 3nx V The string is exited with the Initial velocity equal 6sin v The force acting to the string is expressed by the function 10 x2 sin t + 10 2(х — 5)2 21πχ -10 sint – 10t sin- 2 - 4t2 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.
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