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## Homework Statement

Calculate the frequency of a bead with a mass of

**m**vibrating on a parabolic track equals to y=Ax

^{2}

## Homework Equations

F=ma

## The Attempt at a Solution

Looking at the bead at any point which isn't equilibrium, I have:

1. ma

_{y}=N-mgcosθ

2. ma

_{x}=mgsinθ

I tried to look at a simpler scenario where the bead follows a circular path, in that case I can use small angle approximation to claim that a

_{y}=0 and also sinθ=θ. also, I defined x=lθ where l equals the radius of the circular path.using that info, I can get the d

^{2}θ/dt=(g/l)*θ and the frequency equals to ω=√(g/l).

Now I'm trying to make some assumptions for the parabolic wire. so I'm pretty sure I can use small angle approximation same as above. as for x, I'm thinking about calculating 'x' using line integral, would that be the best way to go or am I should I look at this problem from a different angle?

Thanks..