Stability of Equilibrium

Stability of Equilibrium

Equilibrium depends on the nature of potential energy curve.

### Formula

Stable Equilibrium:

$$\frac{d^2U}{dx^2}>0$$

Unstable Equilibrium:

$$\frac{d^2U}{dx^2}<0$$

Neutral Equilibrium:

$$\frac{d^2U}{dx^2}=0$$

### Terminologies

- Stable Equilibrium → Body returns to equilibrium after small displacement.

- Unstable Equilibrium → Body moves away after displacement.

- Neutral Equilibrium → Potential energy remains constant.

### Usage

- Used in potential energy graph problems.