Holding bead displacement fixed while stiffness changes turns the trap-force rule into three exact rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
One-newton-per-metre trap gives three newtons
Hold displacement at 3 metres. Stiffness 1 newton per metre gives force 3 newtons back toward the trap center.
1⋅3=3
Doubling stiffness doubles the restoring force
The bead stays at the same 3 metre displacement. Stiffness 2 newtons per metre gives force 6 newtons.
2⋅3=6
Three stiffness rows make the force scale visible
With stiffness 3 newtons per metre and the same displacement, the restoring force is 9 newtons. The arrows grow by the same factor as stiffness.