What is the equation of motion for two masses connected by a spring?

The equation of motion for two masses connected by a spring is given by the differential equation (m1ddotx1 k(x1 - x2) 0) and (m2ddotx2 k(x2 - x1) 0), where (m1) and (m2) are the masses, (k) is the spring constant, (x1) and (x2) are the displacements of the masses from their equilibrium positions, and (ddotx1) and (ddotx2) are the accelerations of the masses.