Stable equilibrium of a 4 mass, 6 spring system

• Vbomm
In summary, the conversation discusses a problem with a physics engine that involves a spring/mass system and finding equilibrium in a box-like shape. The writer has tested each spring individually and is considering changing the spring constants along the diagonals, but is unsure of how to proceed. They also mention that the springs have damping, but currently stop in tension instead of coming to rest with no tension.

Homework Statement

I am making a physics engine for my computer science class and couldn't figure out how to get the spring/mass system to come to equilibrium into a box-like shape such as the one on the left. I can understand why the one on the right is in equilibrium but I don't know how to make the system not do that. (Keep in mind, these are ideal springs and point-particles so the springs pass through each other)

All the springs have the same spring constant and there is no force exerted on the particle in the x/y direction if the two particles' x/y components are separated by 0.5m

Homework Equations

Fx(1) = -k[(x2-x1)-0.5] + -k[(x3-x1)-0.5] + -k[(x4-x1)-0.5]
Fy(1) = -k[(y2-y1)-0.5] + -k[(y3-y1)-0.5] + -k[(y4-y1)-0.5] [/B]
and so on...

The Attempt at a Solution

I tested each of the 6 springs individually on their two important masses and it definitely brings them to equilibrium 0.5m apart (in the relevant components -- so for the diagonals technically .707 but still 0.5 in each component)

My intuition tells me that the spring constants along the diagonals should be different but because I am working with components but I feel like because the diagonals work as intended on their own, I should just leave them be.

Not quite sure where I went wrong or what I could change about the diagonals

what is your definition/criterion for equilibrium ?

BvU said:
what is your definition/criterion for equilibrium ?
The springs have some damping so they eventually come to rest and stop moving. Currently they stop moving while in tension while I intend for them to come to rest with no tension.

Why would you expect them to come to rest with no tension ?