Does $$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$ measure the natural frequency or driving frequency of a spring-mass system? I can't find any resources which confirm this!

I believe it measures the driving frequency since it changes depending on the mass held by the spring, however, if so, what is the natural frequency representing? The intrinsic vibrations of the spring?

  • $\begingroup$ It's usual to study Simple Harmonic Motion (an idealisation of Natural Oscillations) before studying the "Forced Oscillations" due to an oscillatory driving force. Haven't you studied SHM? [I'm just trying to understand why you asked your question.] $\endgroup$ – Philip Wood Dec 22 '18 at 16:54

Your equation gives the natural frequency of the mass-spring system.This is the frequency with which the system oscillates if you displace it from equilibrium and then release it.

The driving frequency is the frequency of an oscillating force applied to the system from an external source. Therefore the driving frequency can be anything you choose; there is no formula or equation for it!

If you start to apply, and then continue to apply, a driving force to your mass-spring system, its motion initially will be the sum of oscillations at its natural frequency and oscillations at the frequency of the driving force. As time goes on the oscillations at the natural frequency will die away (because of damping forces) and only the oscillations at the frequency of the driving force will remain.


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