A particle of mass m moving in one dimension has potential energy U(x)=U0[2(x/a)2−(x/a)4], where U0 and a are positive constants.
(a) Find the force F(x), which acts on the particle.
(b) Sketch U(x). Find the positions of stable and unstable equilibrium.
(c) What is the angular frequency ω of oscillations about the point of stable equilibrium?
(d) What is the minimum speed the particle must have at the origin to escape to infinity?
(e) 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) and sketch the result.