Balancing interactivity with springs and weights.
Balance the bar with the three weight on the inside.
Attach weights of 1, 2, 4, and 8 units to the four attachment
points on the bar. Move the bar from side to side until you find a
balance point. Is it possible to predict that position?
If you leave the hook at $X$ empty, what angle does $OX$ make to
the vertical once the balance settles?