k m m H Consider the system shown in the picture. Notice that the middle Y ball is heavier than the side balls. *; X, Start the system with random initial displacements from equilibrium and random initial velocities. 1) Write a code that finds the eigenvalues and eigenvectors for this system. Use them to find positions and velocities for future times. 2) Write a code that finds positions and velocities using velocity Verlet algorithm. Compare results obtained by these two methods