You can simply take the FFT of the data or use one of the spectral VIs such as Amplitude and Phase Spectrum.vi. They are found in the Signal Processing palette and the Spectral or Transforms subpalettes.
Your data looks rather strange. Is it one small data set repeated twice? The result is that there is a dominant component at about 57 Hz but also components at ~1/3 and 2/3 of that frequency as well as harmonics.
In the VI I attached I have padded the data by concatenating arrays of zeros before and after the data set to improve the spectral resolution.
Lynn