Calculate the frequency of a bead with a mass of m vibrating on a parabolic track equals to y=Ax2
The Attempt at a Solution
Looking at the bead at any point which isn't equilibrium, I have:
1. may =N-mgcosθ
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 ay=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 d2θ/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?