Natural Frequency Calculator

Natural frequency is dictated by a system's stiffness and inertial mass. For a foundational spring-mass system, the natural angular frequency ($\omega_n$) is defined as $\omega_n = \sqrt{k/m}$, where $k$ represents the spring constant and $m$ is the mass. Converting angular frequency to standard frequency ($f$) yields $f = \frac{1}{2\pi}\sqrt{k/m}$. For structural beams, equations factor in young's modulus ($E$), area moment of inertia ($I$), length ($L$), and mass distribution (such as concentrated masses or linear density $\rho$), allowing the calculator to handle cantilever, simply supported, and fixed-end configurations accurately.

Consider a spring-mass system where the spring constant ($k$) is 64 N/m and the attached mass ($m$) is 0.5 kg. First, divide the spring constant by the mass: $64 / 0.5 = 128$. Next, take the square root of that result: $\sqrt{128} \approx 11.3137$. Finally, divide by $2\pi$ (approximately 6.28318): $11.3137 / 6.28318 \approx 1.8005$ Hz. Thus, the natural frequency of the system is approximately 1.80 Hz.

Always ensure your units are consistent before entering parameters into the calculator, preferring standard SI units (meters, kilograms, Newtons, and seconds). When evaluating beams, double-check whether your system features a concentrated load or a distributed mass, as picking the wrong configuration will drastically alter the computed frequency. Finally, be mindful of structural damping; while this calculator computes undamped natural frequency, real-world amplitudes will gradually decay over time.