Which factors primarily determine the natural frequency of a mechanical system?

• A. Mass and stiffness
• B. Mass and damping
• C. Damping and stiffness
• D. Temperature and mass

Answer: (A)

Natural frequency is set by how the system stores energy in inertia and in the elastic restoring force. In a simple mass-spring system, the equation of motion is m x'' + k x = 0, which leads to omega_n = sqrt(k/m). This shows that stiff springs (larger k) raise the natural frequency, while a heavier mass (larger m) lowers it. Damping doesn't determine the intrinsic natural frequency; it mainly affects how the system responds over time (it can reduce amplitude and, with heavy damping, slightly shift the observed frequency to the damped value). Temperature can tweak material properties and thus stiffness or mass, but the primary factors that set the natural frequency are mass and stiffness.