An object with a potential energy u(x) can oscillate around
1. any equilibrium point.
2. any stable equilibrium point.
3. any point.
4. any unstable equilibrium point.
5. certain stable equilibrium points.
6. any point provided that the restoring force exerted on the object is given by hooke’s

Any stable equilibrium point

Explanation:

I actually just got this as a homework question in Quest. Pendulums and such don't use Hooke's law, so we can rule that out. We can also rule out unstable equilibrium points, because those wouldn't cause an oscillation. Think of a rollercoaster on top of a hill. The top is an unstable equilibrium, and the cars don't roll back up after being displaced. We can rule out "Any equilibrium point" because that includes unstable points. Same explanation goes for "any point."  That leaves "certain stable equilibrium points" and "any stable equilibrium point." I honestly don't even know what the "certain" stable point answer means. I don't know why certain stable equilibrium points would be better than others. So, by process of elimination, we are left with "any stable equilibrium points."