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A bit of solid state physics: Chain of atoms. This continues the example in "Application: Normal modes" in the Intro to matrices handout. (a) (This part is a paper problem, not a computer problem.) Derive the eigenvalue equation that must be solved when there there are five springs k and four masses m all in a row. Partial solution: The equation will invol ve the matrix 2 -1 0 0 1 2 -1 0 0 -1 2-1 0 0 -1 2 (b) Generalizing this pattern, write a program that computes the ma- trix when there are N masses and N +1 springs in a row. Have your program ask for N, then print out the matrix and the N val- ues of for the normal modes, and try it out with, for example. N- 10. A bit of solid state physics: Chain of atoms. This continues the example in "Application: Normal modes" in the Intro to matrices handout. (a) (This part is a paper problem, not a computer problem.) Derive the eigenvalue equation that must be solved when there there are five springs k and four masses m all in a row. Partial solution: The equation will invol ve the matrix 2 -1 0 0 1 2 -1 0 0 -1 2-1 0 0 -1 2 (b) Generalizing this pattern, write a program that computes the ma- trix when there are N masses and N +1 springs in a row. Have your program ask for N, then print out the matrix and the N val- ues of for the normal modes, and try it out with, for example. N- 10