\[f_r=\frac{1}{2\pi}\sqrt{\frac{k}{m}}\]
Variables
frresonant frequency (Hz)
kspring constant (N/m)
mmass (kg)
Description
What is this formula?
The Resonant Frequency of a Mass-Spring System calculates the natural frequency at which a mass attached to a spring oscillates when disturbed. At this frequency, the system can exhibit large oscillation amplitudes if externally excited.
When to use it
Use this formula when analyzing vibrations, mechanical oscillators, suspension systems, machinery, and dynamic systems involving springs and masses.
Example
Given:
k = 1000 N/m
m = 2 kg
Formula:
fr = (1/(2π))√(k/m)
Substitution:
fr = (1/(2π))√(1000/2)
fr = (1/(2π))√500
fr = 3.56 Hz
Result:
fr ≈ 3.56 Hz
Applications
Mechanical vibration analysis.
Vehicle suspension systems.
Machine design.
Structural dynamics.
Resonance studies.