Let a particle of unit mass be subject to a force x- x3 where x is its displacement from the coordinate origin. (a) Find the equilibrium points, and tell whether they are stable or unstable. (b) Calculate the totalenergy of the particle, and show that it is a conserved quantity. (C) Calculate the trajectories of the particle in phase space.

Let a particle of unit mass be subject to a force x- x3 where x is its displacement from the coordinate origin. (a) Find the equilibrium points, and tell whether they are stable or unstable. (b) Calculate the totalenergy of the particle, and show that it is a conserved quantity. (C) Calculate the trajectories of the particle in phase space.