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. 7nx 17nx V Initial displacement of the string is equal -3sin- + 8sin- 10 x2 Зих + 2 V The string is exited with the Initial velocity equal 6sin V The force acting to the string is expressed by the function 21 πχ -10 sint – 10t sin- 2 x2 sin t + 10 2(x – 5)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).
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. 7nx 17nx V Initial displacement of the string is equal -3sin- + 8sin- 10 x2 Зих + 2 V The string is exited with the Initial velocity equal 6sin V The force acting to the string is expressed by the function 21 πχ -10 sint – 10t sin- 2 x2 sin t + 10 2(x – 5)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).
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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Question
Write appropriate Transformation ?(?, ?) for the Step 1.
Finalize Step 1 and specify the problem for ?(?, ?).
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.
7nx
17nx
V Initial displacement of the string is equal -3sin-
+ 8sin-
10
x2
Зих
+
2
V The string is exited with the Initial velocity equal 6sin
V The force acting to the string is expressed by the function
21 πχ
-10 sint – 10t sin-
2
x2
sin t +
10
2(x – 5)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).
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