# Error in FFT (Sectrum) analyzer Instrument

Recently I performed an experiment on finding the natural frequency of vertical cantilever. I used accelerometer and FFT analyzer instrument for measuring it. First I kept the accelerometer near the top edge of the vertical cantilever and a slight vibration was given and obtained the experimental value of natural frequency as 25.5 KHz for three consecutive times. Then I kept the accelerometer below the middle portion of the beam and conducted experiment thrice resulting in the experimental natural frequency as 25.75 KHz. What could be the reason for these error? The instrument shows same reading at same place, no matter how many times the experiment is being done but different places shows different natural frequency of the same vertical cantilever beam. What could be the technical explanation behind it? The answer also vary from the theoretical value obtained as 31 KHz. I used DI 2200 FFT realtime analyzer model for performing the experiment.

• Can you provide a picture or sketch? – garyp Mar 27 '19 at 15:29
• The error you are seeing between your measurements is just 1% which is normally acceptable in engineering terms, you should check the accuracy of the device you are using, see what is the usual error rate. – S V Mar 27 '19 at 15:53
• The reason you could be observing the difference might also be the presence of another mode of vibration with a smaller amplitude, you should check where the nodes are. Also the beam equation is normally simplified to a linear fourth order under the assumption of homogeneity, but if your beam did not receive an annealing process then it's most likely not homogeneous and also anisotropic. In that case you would have to consider $E$ to be a rank 2 tensor rather than a scalar. – S V Mar 27 '19 at 15:59