Question

If a particle moves in a potential energy field U = U₀ – ax+ bx² , where a and b are positive constant, obtain an expression for the force acting on it as a function of position.At what point does the force vanish? Is this a point of stable equilibrium?

Calculate the force constant and frequency of the particle.

Answer 1

i.e., a x = a / 2b is a point of minimum potential energy. Hence, the equilibrium is stable.

k = 2b