What are normal modes?

Normal modes are special ways that things can move together in harmony.

Imagine you're pushing a swing. If you push it just right, it goes back and forth smoothly, that's one way it can move. But if you have two swings side by side, and you both push them at the same time, they might start moving in different patterns: maybe one goes high while the other stays low, or they both go up and down together.

A normal mode is when all the parts of something move in the same rhythm, like how your legs move when you walk. If you have two swings connected by a rope, they can move as one big system. In a normal mode, both swings swing at the same time, either going up and down together or moving in opposite directions.

It’s like when you shake a jumping castle, if you do it just right, the whole thing bounces in one smooth motion, and that's its special way of moving, its normal mode.