Ok, so the system is a ring with four identical springs connected to a single mass. Each spring is in a different quadrant and at an angle alpha from the horizontal. L is the relaxed length of each spring, k' is the spring constant, and R is the radius of the ring. and ignore gravitational and frictional forces.(adsbygoogle = window.adsbygoogle || []).push({});

See diagram

The mass is oscillating in the x direction only.

I am trying to find and equation for the potential energy and the sum of the forces from each spring but I can never get it right.

The paper that this came from is "mechanical analogs to the landau zener model" by Shore et al. Init he has the potential energy as

[tex]U=k'(2(R-L)^{2} + 2(1-\frac{L}{R}sin^{2}(\alpha))*x^{2})[/tex]

I've tried finding the displacement and putting it into [tex]U=\frac{1}{2} kx^{2}[/tex] and ive tried finding the sum of the forces and [tex]U=-\int {F \bullet dx}[/tex]. Neither gave me anything close to the paper.

If anyone could help me out that would be great. Thanks.

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# Potential energy of mass spring system

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