Why does a system have a natural frequency?

Natural Frequency Calculator

An infinite number . The number of natural frequencies an object can have depends on its flexibility in different directions and degrees of freedom. In any one direction it can have one fundamental mode and many harmonics.

All stable, unforced, mechanical systems vibrate harmonically at certain discrete frequencies , known as natural frequencies of the system. A system with three masses would have three vibration frequencies, and so on. In general, a system with more than one natural frequency will not vibrate harmonically.