Question #1

Question #2

Consider waves on a string of length L with tension T, and variable mass density (x)=0exp(x/L) with T=50N;0=0.003kg/m;L=3.2m In both parts of this problem the boundary condition at x=0 is y(0)=0 Hint: You will need to think about how to modify your B matrix to do these problems. Just using the form from the Labs won't work. At x=L a massless transverse spring is attached to the end of the string with spring constant k=16N/m which produces the boundary condition Txy=kyatx=L Write a program to find the first 3 normal mode frequencies and eigenfunctions for this system. Plot these three eigenfunctions, and put their frequencies in the title of the plot. Write clean, readable code, as you will be graded on both readability of your code and its functionality. Upload your Python file here. Now the spring is removed and a mass m=0.003kg is attached at x=L. This produces the boundary condition mt22y=Txyatx=L Write a program to find the first 3 normal mode frequencies and eigenfunctions for this system. Plot these three eigenfunctions, and put their frequencies in the title of the plot. Write clean, readable code, as you will be graded on both readability of your code and its functionality. Upload your Python file here