Measurement of low frequency mechanical vibrations based on an inverted magnetic pendulum

Abstract

In this paper is presented the mathematical model, design and construction of a prototype of a  vibration frequency meter in an adjustable range of 2 Hz to 30 Hz; The experimental results and their analysis are also presented, making a comparative evaluation with the theoretical model. The device is based on the principle of resonance applied in an inverted magnetic pendulum whose natural frequency can be modified by variations of physical parameters. The oscillation of the pendulum is recorded detecting variations in the magnetic field using hall effect sensors; the data recorded with a microprocessor is analyzed and the results are simultaneously plotted in a computer interface. The data obtained were processed to be plotted in the frequency domain, facilitating its analysis. It was proved that the prototype can be used as a frequency meter and that the adjustable character of the device works according to the mathematical model. Finally, The effect of the friction force was studied, it was concluded that the friction force affects the measurement after a considerable period of time of oscillation, but not in the first moments.