What best describes the natural frequency of a machine?

• A. The rate at which a mechanical system tends to oscillate in the absence of external forcing
• B. The rate of external forcing applied to the system
• C. The damping coefficient of the system
• D. The resonance frequency observed under continuous load

Answer: (A)

Natural frequency is the intrinsic rate at which a mechanical system tends to vibrate when it is displaced and released, with no continuous external forcing. It depends on the system’s stiffness and mass (for a simple mass–spring, ωn = sqrt(k/m), and fn = ωn/2π). This means the system has a natural tendency to oscillate at this rate regardless of how you try to drive it. External forcing can excite the system at various frequencies, and damping affects how the motion dies out or how the peak response appears, but doesn’t change the inherent rate set by mass and stiffness.