In a conservative force field the relation
in force and potential energy is given as F = – dU/dx so if at a point in
conservative force field there can be three general conditions for which force
on a particle becomes zero.

Case
– I : When U = Constant

In this case the U vs x curve will be a
section of horizontal straight line in which there is no change in potential
energy if body is displaced slightly on this section where potential energy is
constant. Thus the gradient of potential energy or Force on particle is zero
and such a position for particle is called the state of neutral equilibrium
when it does not experience any force on displacement in a force field.

Case
– II : When U is Maximum

In this case the tangent to U vs x curve
will have zero slope and again force on particle at this position will be zero
but when the particle is displaced from this position in either direction,
particles potential energy decreases so particle will experience a force in the
direction away from the maximum potential energy position. Such a position as
force is zero it is in equilibrium but if particle is displaced, it tend to
move away from this position so it is called the state of unstable equilibrium.

Case
– III : When U is Minimum

In this case also the tangent to U vs x
curve will have zero slope and again force on particle at this position will be
zero but when the particle is displaced from this position in either direction,
particles potential energy increases so particle will experience a force in the
direction toward the minimum potential energy position. Such a position as
force is zero it is in equilibrium but if particle is displaced, it tend to
move toward this position so it is called the state of stable equilibrium.

Lets understand the Concept of Equilibrium
through this video https://youtu.be/_tUvRNxuYkg

To understand the
application of Equilibrium concept follow the Example Videos below –

https://youtu.be/48mc6p-M5y8

https://youtu.be/Tju6_kDHRqE

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