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If an object is in mechanical equilibrium and at rest, then it will remain at rest. However, if the object is displaced (moved) slightly away from equilibrium, then one of two things may happen depending on whether the equilibrium is stable or not.

If an object is in mechanical equilibrium and at rest, then it will remain at rest. However, if the object is displaced (moved) slightly away from equilibrium, then one of two things may happen depending on whether the equilibrium is stable or not.

If the equilibrium is stable, then the potential near the equilibrium point is like a bowl: around the centre of the bowl (the equilibrium point) the potential is greater than at the equilibrium point and the object moves back to equilibrium. This is true if the second [[derivative]] of the potential is less than 0. An example of this is [[simple harmonic motion]] and another is a ball in a bowl.

If the equilibrium is stable, then the potential near the equilibrium point is like a bowl: around the centre of the bowl (the equilibrium point) the potential is greater than at the equilibrium point and the object moves back to equilibrium. This is true if the second [[Derivative_(calculus)|derivative]] of the potential is less than 0. An example of this is [[simple harmonic motion]] and another is a ball in a bowl.

If the equilibrium is unstable, the potential is like an upside down bowl. If the object is displaced slightly, then it moves further and further away from the equilibrium point. This occurs when the second derivative in greater than 0. An example of this is a ball rolling off an upside down bowl.

If the equilibrium is unstable, the potential is like an upside down bowl. If the object is displaced slightly, then it moves further and further away from the equilibrium point. This occurs when the second derivative in greater than 0. An example of this is a ball rolling off an upside down bowl.