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Math Help - two-body spring problem

  1. #1
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    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. >_<
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  2. #2
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    Quote Originally Posted by Zizoo View Post
    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 ?
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  3. #3
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    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....
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