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Natural frequency refers to the frequency at which a mechanical system naturally vibrates when it is disturbed from its rest position and then allowed to oscillate freely without any continuous external force acting upon it. Each mechanical system has its unique set of natural frequencies, which are determined by the system's mass, stiffness, and damping characteristics.

In this context, when a system is displaced and then released, it will oscillate at these natural frequencies until energy is dissipated, typically due to damping forces. Understanding natural frequency is crucial in vibration analysis because it helps engineers design systems to avoid resonance, which occurs when the frequency of external forces matches the natural frequency of the system. This can lead to excessive oscillations and potentially catastrophic failures.

In contrast, other options focus on varying aspects of vibrational behavior but do not accurately represent the concept of natural frequency. For instance, the yielding frequency pertains to material properties under stress, while resonance relates to the interaction between external forcing frequencies and natural frequencies, highlighting a more dynamic interaction rather than the intrinsic property of the system itself. The maximum frequency a system can sustain is more related to structural limits than the defined concept of natural frequency.