1. A particle moves in one dimension and is subject to a conservative force, whosepotential energy function is given by U(x), where a and b are positive constants.U(r) = ax' – bxax³a) Find the two equilibrium positions of the particle.b) For each of the two equilibrium positions, determine whether the equilibrium isstable or unstable.

For equilibrium points we have to calculate force from the potential energy and equate it with zero…

1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. ax - bx U (x) = a) Find the two equilibrium positions of the particle. b) For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.

1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. ax - bx U (x) = a) Find the two equilibrium positions of the particle. b) For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.