Understanding Particle Motion and Stable Equilibrium in a Potential Energy Graph

[darksummoning]

im so lost with this question, i have tried a lot and cannot solve it :

A particle of unit mass moves on a straight line under a force having potential energy V (x) =
x3=(x^4 + a^4) where  and a are positive constants. Sketch the graph of V (x).
(a) Find the period of small oscillations about the position of stable equilibrium
(b) Suppose the particle passes the origin, moving in the positive x-direction with speed v[0]. Show
that the particle will subsequently pass the point x = a if and only if v^2[0] > =a. Find a further
condition on v^2[0] for the particle to subsequently pass the point x = -a

(square brackets represent a subscript)

Thansk in advance----aa.

 

[ideasrule]

First, V (x) =
x3=(x^4 + a^4) doesn't make sense. Which one is V(x) equal to:
x3 or (x^4 + a^4)?

For (a), force varies linearly with displacement according to F=-kx near the equilibrium point. (Can you see why?)

(b) Sounds a lot like a conservation of energy problem!

 

[darksummoning]

hi sorry about the messy question... i have added it as an attatchement. i managed to do the first part but cannot seem to do the the last part of part b.