申論題

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.