(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Alright so I've got a potential energy equation U(x) = E/β^4(x^4+4βx^3-8(β^2)x^2) and U'(x) = E/β^4[4(x^3) + 12β(x^2) - 16(β^2)x] (where β and E are constants) that describes a particle of mass m which is oscillating in an energy well. I solved for where the system has equilibrium positions through simple differentiation of U(x). (an equilibrium is at x=β and x=-4β) Now I have to find the angular frequency about each equilibrium position and estimate how small the oscillations should be around the equilibrium position.

2. Relevant equations

N/A

3. The attempt at a solution

I figure that since dU/dt = ma, I can differentiate U(x), equate it to acceleration, and solve for ω. However, the equation for U(x) is rather messy, and I still don't know across which distance the particle is oscillating. Any ideas?

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# Homework Help: Finding angular frequency about the equilibrium position.

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