# Mass Spring System

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Hi there. For about half a year now, I'm trying to think about a solution for this topic. I guess I figured out something that sounds promising... but it pretty much forces me to find the equilibrium point of a spring system. A number of spring connections given, how do you find that mass' natural eq. point? I'm talking about a single mass and its material constaints. I took the approach of a (Force)Vectorfield that is generated by the springs. setting the derivative to zero would give us the eq. point. But as easy as it sounds...just three connections are enough to let the equations explode! Any idea?

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Is this a simulation that has to run realtime? Doing things the force field way seems overly complicated to me, though if you do go that route, there are any number of general solver methods that could help (see Numerical Rescipies online)

In my opinion, the easier way is to run an iterative solver. Simulate a point mass, connected by springs to some fixed points. At every step of the solution, calculate the sum of the forces acting upon the point, and move it a bit in that direction (you do not need to be physically correct here, and keep track of momentum: if you go this route, just scale the sum of the forces by some small constant so it will be stable). Repeat until the sum of the forces falls below some threshold.

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Well here's ma idea:

The problem of mass spring systems (as you described one) is that the stiffness is indirect proportional to the time step. (or somthing like that)
That requires an enourmous cpu load if you wanna simulate metal materials for examle.

So I figured why not using a dampened oscilation to get an accurate position of the mass point after any time step???

There's only the problem of the force that point is creating on its neighbor by this oscilation.

But I didn't even get that far.
Turns out that you (of course) need an equilibrium point to be able to make ot oscillate around that point.

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Rutin
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JoeJ
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