1. ## two-body spring problem

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).

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

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. >_<

2. Originally Posted by Zizoo
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).

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

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. >_<
Hi

If you subtract the 2 equations you will get

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

which means that $x_1 - x_2$ is a solution of $\frac{d^2X}{dt^2} = 2kX$

Does this help ?

3. Hm, yes, I suppose it does. I keep trying to build myself up to other, harder problems I have to solve eventually for my game with smaller steps, but the answers can't really be applied in the higher-level issues.

I wanted to find Taylor polynomials for the motion of objects in a game with gravitation (high gravitational constant) and spring forces and maybe some other stuff, but I'm starting to think I may just need to find a way to break the linear approximations into smaller steps between frames or something....