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## Homework Statement

A particle of mass m is oscillating with amplitude A in 1D (without damping). Using conservation of energy, I'm asked to determine the period T with the correct proportionality factor and period of integration.

## Homework Equations

Potential energy: [itex] U(x) = a x^2 + b x^4 [/itex] where a > 0 and b ≥ 0

Period: [itex]T(A) \propto[/itex]∫[itex]\frac{dx}{\sqrt{E(A) + U(X)}}[/itex] (from conservation of energy)

## The Attempt at a Solution

I scribbled down a few attempts but none of them went anywhere. I don't have the slightest idea where to start so I'm hoping someone can point me in the right direction.

I think that's all the information provided, but feel free to ask if you have any questions. It's my first time posting here, my apologies if I haven't follow proper rules or etiquette.

Thanks