A particle, of mass m, is moving in one dimension under the influence of a conservative force with potential V (x). (a) If the potential is given by V (x) = x² – xª, (2) find any equilibrium points and determine their stability. (b) The particle is started from the origin x = 0 with speed v, and moves under the influence of the potential V (x) defined in equation (2). How large does v need to be for the motion to be unbounded?

A particle, of mass m, is moving in one dimension under the influence of a conservative force with potential V (x). (a) If the potential is given by V (x) = x² – xª, (2) find any equilibrium points and determine their stability. (b) The particle is started from the origin x = 0 with speed v, and moves under the influence of the potential V (x) defined in equation (2). How large does v need to be for the motion to be unbounded?