Consider an object that is initially at rest with a net force on it that is zero. The object is
given a push
The object will then oscillate harmonically
about the initial position
1. as if it were any stable equilibrium point
and the push was small.
2. as if it were an unstable equilibrium and
the push was small.
3. as if it were any equilibrium point and the
push was small
4. as if it were any equilibrium point, re-
gardless of the size of the push.
5. for all such initial points where the net
force on the object was zero.