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Decoration-concentric waves as symboll for vibration. Image source:

Piezo Accelerometer Tutorial

What is Vibration?

Basics of Vibration 1


A body is said to vibrate when the body as a whole or parts of it are oscillating about a rest position. (For the moment we are looking at oscillations that are cyclic or periodic.)


The number of times a complete motion cycle takes place during one second is called frequency.

The dimension of the frequency is called Hertz

1 Hertz equals to 1/sec (or 1 cycle per second)


If the oscillating motion consists of a single component occurring at a single frequency, like for example a tuning fork, the motion is called harmonic or sinusoidal.


The vibration of a real machine is normally much more complex and consists of many components with different frequencies occurring simultaneously.


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Three different Ways to describe Sinusoidal Vibration

In the following we will explore the sinusoidal vibration in more details. There are three different notations to describe and quantify the vibration: Displacement, velocity and acceleration


The correct notation of a sinusoidal displacement d (motion) is:


d = D sin (ωt𝛗)


D = amplitude

ω = angular frequency ω = 2π∙f

f = frequency   f = 1 / T

φ = phase

We can normally consider that φ = 0

so d becomes:


d = D  sin ωt

The displacement vs time is a sine or sinus

The notation "sin ωt " is arbitrary, sometimes "cos ωt " is used in place.



The velocity is another mean to describe vibration

The velocity is of course also a sine function. It is leading* the displacement with a phase shift of π/2.

v = V ∙ sin (ωt + π / 2)


this is identical to


v = V ∙ cos ωt


V = velocity amplitude

ω = angular frequency ω = 2π∙f

= frequency = 1 / T

*) We could also say the displacement is lagging the velocity


Note: The scale of the velocity amplitude has been chosen in a way that it appears eaqual to the displacement amplitude



A third mean finally to describe vibration is the acceleration

The acceleration is sinusoidal with a phase shift of half a cycle or π with respect to the displacement.


a = A ∙ sin (ωt + 𝛑)


this is identical to

a = − A ∙ sin ωt *


* The negative sign is indicating that for the harmonic motion the acceleration is always in opposition to the displacement.

The acceleration points exactly in the opposite direction of the displacement

Note: The scale of the acceleration amplitude has been chosen in a way that it appears equal to the displacement amplitude

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