3. (20%) Three particles of identical mass m are connected by springs and attached to non-moving walls as shown in Fig. 1. All the springs are identical and have a spring constant k. The forces exerted on particles obey hooks law. Gravitation is neglected. Find the equation of motion for the three particles deviating from their equilibrium positions (x1, X2, x3 in Fig. 1), respectively and find the eigenfunctions and corresponding eigenvalues of the oscillator system.
