Two particles are bound to one another by a spring that is at equilibrium only when the two particles are adjacent (effectively in the same location).

$\displaystyle \frac{d^2x_1}{dt^2} = -k(x_2-x_1)$

$\displaystyle \frac{d^2x_2}{dt^2} = -k(x_1-x_2)$

I haven't got the slightest idea what to do. Every manipulation I've tried has been a dead end, leading to something like 2=2 or something similarly stupid. >_<