A mass m hangs from the ceiling via a spring of spring constant k. A second mass m hangs from the first via a second spring of spring constant k. Any friction is completely negligible. x is the displacement of the upper mass from its equilibrium position, and x2 is the displacement of the lower mass from its equilibrium position. (a) Write the equations of motion (Newton's second law) for each mass. (b) By assuming that the masses' displacements from their equilibrium positions vary in time sinusoidally with angular frequency w, find the eigenvalues of these equations. (c) Determine the corresponding eigenvectors.