# Sinusoidal vibration: interrelation of acceleration, velocity and displacement parameters

In the course of tests performance based on the use of a harmonic signal (e.g., during calibration of the vibration transducers), it is necessary to take into consideration the interrelation of vibration displacement, velocity, and acceleration parameters.

Let us denote the displacement amplitude as S (mm), vibration velocity amplitude as V (cm/s), and vibration acceleration amplitude as A (m/s2), then:

 V = S·2πf/10 (cm/s) A = S·(2πf)2/1000 (m/s2),

where f — frequency, Hz.

For instance, at the frequency of 50 Hz, the displacement of 1 mm will correspond to the velocity of 31 cm/s and the acceleration of 99 m/s2.

The interrelation of acceleration parameters is specified below:

 g m/s2 cm/s2 1 9,81 981 0,102 1 100 0,00102 0,01 1

In addition to the formulas, it is also possible to use a nomographic chart with a graphical display of the interrelation between various parameters of the mechanical oscillations, i.e., between frequency, displacement, velocity, and acceleration of the harmonical mechanical oscillations. Based on the values of these two parameters and using this nomographic chart, it is possible to obtain the values of the two unknown parameters of the mechanical oscillations.

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