Different types of equilibrium are −

Stable :

(i) When a particle is displaced slightly from a position, then a force acing on it brings it back to the initial position, it is said to be in stable equilibrium position.

(ii) Potential energy is minimum.

(iii) \(\frac{d^2U}{dx^2 }= positive\)

(iv) E.g. A marble placed at the bottom of a hemispherical bowl.

Unstable :

(i) When a particle is displaced slightly from a position, then a force acting on it tries to displace the particle further away from the equilibrium position, it is said to be in unstable equilibrium position.

(ii) Potential energy is maximum

(iii) \(\frac{d^2U}{dx^2 }= negative\)

(iv) e.g. a marble balanced on top of a hemispherical bowl.

Neutral :

(i) When a particle is slightly displaced from a position it does not experience any force acting on it and continues to be in equilibrium in the displaced position, it is said be in neutral equilibrium

(ii) Potential is constant

(iii) \(\frac{d^2U}{dx^2 }= 0\)

(iv) e.g. A marble placed on a horizontal table.