Natural frequency is the frequency at which a system oscillates when not subjected to a continuous or repeated external force. It is determined by the system's physical properties such as mass and stiffness.
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Every oscillatory system has its own natural frequency, which depends on its physical characteristics.
When an external force matches the natural frequency, resonance occurs, leading to a significant increase in amplitude.
In mechanical systems, natural frequency can be calculated using $f_0 = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$, where $k$ is the stiffness and $m$ is the mass.
Electrical systems also have natural frequencies determined by inductance and capacitance, given by $f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{LC}}$.
Identifying and controlling natural frequencies is crucial in engineering to avoid destructive resonant conditions.