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Natural Frequency
Natural frequency or eigenfrequency is the frequency at which a system tends to oscillate in the absence of any driving force.
The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinusoidally with that same frequency).
If the oscillating system is driven by an external force at the frequency at which the amplitude of its motion is greatest (close to a natural frequency of the system), this frequency is called the resonant frequency.
Angular frequency, \(\large \omega = 2 \pi f\)
Examples
For a mass-spring system of mass \(\large m\) and stiffness \(\large k\), the natural angular frequency can be obtained by:
\(\large \omega_0 = \sqrt{\dfrac{k}{m}}\),
In LC and RLC Circuits, its natural angular frequency can be calculated as:
\(\large \omega_0 = \sqrt{\dfrac{1}{LC}}\),