I've been looking at a coupled harmonic oscillator, and normal modes of this: http://en.wikipedia.org/wiki/Normal_mode#Example_.E2.80.94_normal_modes_of_coupled_oscillators At the bottom of this example it says: This corresponds to the masses moving in the opposite directions, while the center of mass remains stationary. The general solution is a superposition of the normal modes where c1, c2, φ1, and φ2, are determined by the initial conditions of the problem. What is the best way to determine these coefficients, given some initial conditions (start position and velocity)? This is only for two masses, but the method should also work for n equal masses. It is fine if I need to program me out of it, but how should i do this?