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

A particle of mass moving in one dimension has potential energy ##U(x)=U_0[2(x/a)^2-(x/a)^4]##, where #U_0# and ##a## are positive constants.

(i)What is the angular frequency ##w## of oscillations about the point of stable equilibrium?

(ii)What is the minimum speed the particle must have at the origin to escape to infinity?

(iii)At ##t=0## the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find ##x(t)##

3. The attempt at a solution

I have no idea about (i), though I know the stable equilibrium point is x=0.

My result of (ii) is ##\sqrt{\frac{-2U_0}{m}[2(x/a)^2-(x/a)^4]}##

But, here comes the problem. The speed at x=0 is 0, so it must stay at the origin forever.

I might get something wrong in obtaining the expression of (ii).

Any help would be appreciated.

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# Stable equilibium of a potential

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