Given a problem of the time dependent forced vibrations of the finite string as follows: Length of the string is equal 4, tension is 180 and density is equal 3. On the left hand end of the string it is given a force equal t and on the right hand end of the string it is given a force equal -sint. Initial displacement of the string is equal 10cos 8cos . 2 17 4 3x The string is exited with the Initial velocity equal 15cos. 2 The force acting to the string is expressed by the function 4 15 sint +21tcos- +15t + x 8 x 8 (x-4} 8 sin t. 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.