\[f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}\]
Variables
foscillation frequency (Hz)
kspring constant (N/m)
mmass (kg)
Description
What is this formula?
This formula calculates the natural frequency of a simple harmonic oscillator made of a mass attached to a spring.
When to use it
Use this formula for ideal spring-mass systems where damping is negligible and the restoring force is proportional to displacement.
Example
Data:
k = 200 N/m
m = 2 kg
Formula:
f=(1/(2*π))*√(k/m)
Substitution:
f=(1/(2*π))*√(200/2)
Result:
f=1.59 Hz
Applications
Mechanical vibrations
Spring-mass systems
Machine dynamics
Suspension systems
Physics education