What is Resonant Frequency?

Resonant frequency ($f_r$) is a fundamental concept in physics and engineering, particularly in the study of oscillating systems. It is the natural frequency at which a system tends to oscillate in the absence of any driving or damping forces. When an external force is applied to the system at or near this natural frequency, the amplitude of the oscillations becomes much larger than at other frequencies. This phenomenon is known as resonance.

For a simple mass ($m$) attached to an ideal spring with a spring constant ($k$), the resonant frequency is determined solely by these two parameters. The system will oscillate at this frequency, given by the relationship:

Understanding $f_r$ is crucial in fields ranging from structural engineering (to avoid catastrophic failures due to resonance in buildings or bridges) to electrical engineering (tuning radio circuits) and even acoustics.

How to Use This Calculator

1. Determine the Spring Constant ($k$): Measure or determine the spring constant of your system in Newtons per meter (N/m). The spring constant relates the force on the spring to its displacement, as defined by Hooke’s Law: $F = -k x$.
2. Determine the Mass ($m$): Measure the mass of the object attached to the spring in kilograms (kg).
3. Enter Values: Input the numerical value for $k$ into the “Spring Constant” field and the numerical value for $m$ into the “Mass” field.
4. Calculate: Click the Calculate Resonant Frequency button.
5. Review Results: The calculated resonant frequency ($f_r$), in Hertz (Hz), will be displayed below, along with the rendered mathematical expression for verification.

Note: This calculator assumes an ideal system with negligible damping and mass of the spring.