Stable equilibrium of a 4 mass, 6 spring system

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.
  • #1
Vbomm
2
0

Homework Statement


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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
 
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  • #2
what is your definition/criterion for equilibrium ?
 
  • #3
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.
 
  • #4
Why would you expect them to come to rest with no tension ?
 

FAQ: Stable equilibrium of a 4 mass, 6 spring system

What is a 4 mass, 6 spring system?

A 4 mass, 6 spring system is a mechanical system that consists of 4 masses connected by 6 springs. The masses and springs are arranged in a specific configuration to create a stable equilibrium.

What is a stable equilibrium?

A stable equilibrium is a state in which a system is balanced and will return to its original position or state if disturbed. In a 4 mass, 6 spring system, this means that the masses and springs are arranged in a way that prevents the system from collapsing or moving uncontrollably.

What factors contribute to the stability of a 4 mass, 6 spring system?

The stability of a 4 mass, 6 spring system depends on several factors, including the stiffness of the springs, the mass of the objects, and the arrangement of the masses and springs. The stiffness of the springs determines how much force is required to move the system, while the mass of the objects affects the overall weight and balance of the system. The arrangement of the masses and springs determines the distribution of forces within the system.

How is stable equilibrium achieved in a 4 mass, 6 spring system?

To achieve stable equilibrium in a 4 mass, 6 spring system, the forces acting on each mass must be balanced. This means that the forces exerted by the springs must be equal and opposite to the forces exerted by the masses. Additionally, the arrangement of the masses and springs must be such that any external forces acting on the system do not cause it to collapse or move uncontrollably.

What are some real-world applications of a 4 mass, 6 spring system?

A 4 mass, 6 spring system can be found in a variety of real-world applications, including shock absorbers in vehicles, suspension systems in bridges, and even the human body. The principles of stable equilibrium in this type of system are also applicable in fields such as engineering, physics, and biomechanics.

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