How Do Displacement, Velocity & Frequency Relate ?

As stated, there are some simple mathematical formulas that relate the frequency of the vibration, the amount of movement (displacement), the speed of movement (velocity) and the force generated during the movement (acceleration). The mathematics involved is always handled by the software and hardware but it is illustrative to understand the simple principles involved. Let's first look at the relationship between frequency, displacement amplitude and velocity amplitude.

Consider: A bearing moves back and forth 10 mils (pk-pk displacement). The bearing moves at 10 cycles per minute (the 'frequency). By setting those two variables, you establish a third - namely the speed at which the bearing must travel to satisfy those two conditions.

Consider: Another bearing is moving at 10 mils pk-pk. This bearing moves at 70 cycles per minute. What is the speed of this bearing vs. the first bearing to satisfy those conditions ?  This bearing must have a peak speed of 7x the first bearing. The relationship between the 3 is linear (e.g. if the frequency increases 7x and the displacement remains same, the velocity must increase 7x). So increasing the frequency 7x while leaving the displacement the same results in increasing the velocity at which the bearing must move by 7x.

The point here is simple. There is a direct relationship between the frequency, the displacement and the velocity. Knowing two - any two - allows the third to be mathematically calculated (along with a constant value). Without getting into further examples, the same direct relationship exists between frequency, velocity and acceleration. Therefore, all four of these variables are related - knowing any two allows the other two to be calculated.

Let's look at the practical aspect of the relationship in a more graphic way.