Even though the motion of our 2 bead system can be complex, we can still use the idea of SHM to describe what's going on.
It turns out that our 2 bead system can exhibit simple harmonic motion if it is started out the right way.
In fact, there are exactly two patterns of vibration in which our 2 bead system can exhibit SHM. These special patterns of vibration are termed Natural Modes. The frequencies of the Natural Modes are called Natural Frequencie
Natural Modes: A mechanical system of N degrees of freedom has exactly N Natural Modes, in which the every part of the system undergoes SHM. Any point of the system that remains at rest during the natural mode motion is called a node of that mode