Answer to Question #259087 in Physics for JAY KIN

Question

1. Construct a potential energy diagram given the situation below.

         The potential energy for a particle undergoing one-dimensional motion along the x-axis is

   U(x)=2(x⁴-x²), where U is in joules and x is in meters. The particle is not subject to any non-

   conservative forces and its mechanical energy is constant at E=-0.25 J.

   a) Is the motion of the particle confined to any regions on the axis, and if so, what are they?

   b) Are there any equilibrium points, and if so, where are they? Are they stable or unstable?

Answer 1

(a) The motion of the particle is confined at the regions $(x_1;x_2)$ and $(x_3;x_4)$.

(b) Equilibrium points:

$$\rm A - stable$$

$$\rm B - unstable$$

$$\rm C - stable$$