Paper 4, Section I, C

Dynamics
Part IA, 2007

Sketch the graph of y=3x22x3y=3 x^{2}-2 x^{3}.

A particle of unit mass moves along the xx axis in the potential V(x)=3x22x3V(x)=3 x^{2}-2 x^{3}. Sketch the phase plane, and describe briefly the motion of the particle on the different trajectories.