If a small displacement of a system from the rest position (after getting some energy) results in a small bounded motion about the equilibrium position, then the system is in

Concept:

Stable Equilibrium:

If the body returns to its original position by retaining the originally vertical axis as vertical.

Unstable Equilibrium:

If the body does not return to its original position but moves further from it.

Neutral Equilibrium:

If the body neither returns to its original position nor increases its displacement further, it will simply adapt its new position.

Analysis:

Equilibrium states after small oscillations:

1) A system is in stable equilibrium If a small displacement of a system from the rest position (after getting some energy) results in a small bounded motion about the equilibrium position. 

2) A system is in unstable equilibrium If a small displacement of a system from the rest position (after getting some energy) results in an unbounded motion about the equilibrium position. 

3) A system is in neutral equilibrium If a small displacement of a system from the rest position (after getting some energy) does not let the system to move above or about the equilibrium position.