2. Construct a new “bi-unstable” system with two unstable states and a stable state in between.

One possible example of a "bi-unstable" system with two unstable states and a stable state in between is a pendulum that can oscillate back and forth between two extreme positions but has a stable equilibrium in the middle.

To construct such a system, we can start with a simple pendulum consisting of a mass attached to a rod or string suspended from a fixed point. The pendulum can swing back and forth under the influence of gravity, with the lowest point being the stable equilibrium state.

To make the pendulum bi-unstable, we can add two magnets to the sides of the pendulum. These magnets repel each other, creating a force that pushes the pendulum away from the center. We can adjust the strength of the magnets so that the force is strong enough to overcome the gravitational force in the middle, but not strong enough to keep the pendulum from swinging past the two extreme positions.

Now, the pendulum has three equilibrium states: two unstable states where the magnets push it away from the center, and a stable state in the middle where the gravitational force balances the magnetic force. If we give the pendulum a small push, it will start oscillating back and forth between the two unstable states, but eventually settle into the stable equilibrium state in the middle. This system is bi-unstable because it has two unstable states and a stable state in between.