# Using the Fourier transform to find the natural frequencies of coupled oscillators

How can I find the natural frequencies of a system consisting of a pair of coupled oscillators using Fourier transforms?

The System consists of two masses and three springs. One of the springs connects the two masses, while the other two springs connect one mass each to a static point. The system is then set free to oscillate. The oscillation is approximately one dimensional.

I have measured data consisting of the position of each mass as a function of time. The measurement frequency was 10Hz.

I understand I'm supposed to transform just the position data (which is periodic). What am I supposed to plot this result against? I do no understand how I can get a proper frequency axis to plot my data with.

I have Octave at my disposal for calculations.

• The overall answer is quite simple; just make a Fourier transfor of your data and find the frequencies of two most dominant peaks (if you weren't unlucky enough to excite only a single mode at your experiment). MATLAB fft function documentation, which @Martijn Pot refers to, contains great examples which answer your difficulties of units conversion. Also, notice that in some cases "fftshift" function is needed to bring some sense to Fourier data. (Don't forget to address the uncertainties in your results!) – Alexander Jul 2 '16 at 2:26

## 1 Answer

Octave is supposed to be very similar.