Piezo Accelerometer Tutorial

What is Vibration?

What is Vibration?

Before we look into accelerometers we want to get a basic understanding of the physics of vibration.

In some places it will be necessary to dive into the theory (sorry for that) but if you don't understand every detail you still can continue.

If you don't have a technical background please use the green path. It is leading logically trough all subjects and touching a basic level of understanding.

In some places there is a yellow path going to some deeper level. If green is too easy for you then the yellow path and red pages might be more suitable for you.

The red pages contain additional mathematical information.

## Physics of Vibration

Acceleration

Acceleration has something to do with movement.

The physical movement of a body can be described with the velocity v of that body.

The velocity has a magnitude (i.e. how fast the body is moving) and a direction (i.e. where the body is moving to).

Such a physical quantity is called a vector and is represented by an arrow whose length corresponds to the magnitude and is pointing in the direction.

If the velocity (in magnitude and direction) is constant the body is moving steadily. We say it is in uniform movement. However the velocity can also change with time.

The change in velocity Δv of a body (either in it’s magnitude or in the direction) during the time period Δt is called acceleration a.

a = Δv / Δt

Δv = v2 -v1 Δt = t2 -t1

The Greek letter Δ (Delta) is used in maths to indicate a difference between to values. Here namely the difference between the velocity v1 at the time t1 and v2 at t2.

The velocity is measured in meters per second m/s.

The dimension of the acceleration (change in velocity per second) becomes therefore meters per second per second

m/s/s or m/s²

The acceleration is also a vector.

I.e. it has a magnitude and a direction.

At time t1 the velocity of the car is v1, at the time t2 it is v2. The acceleration a is the change in velocity between t2 and t1

The acceleration is the difference of the velocities at t2 and t1 divided by the time difference t2 - t1

This is to contunue on the yellow, more advanced path

If you like more maths, try out the

### Sir Isaac Newton

A particular acceleration that we feel every day is the gravity of the earth which makes things fall down on the ground when they are let go.

Sir Isaac Newton, an English physicist and mathematician formulated the laws of motion and universal gravitation in 1687.

Newton himself often told the story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree.

The gravitational acceleration is 1g = 9.81 m/s²

Isaac Newton © by Wikipedia, the free encyclopedia

Other ground-breaking apple stories:

### Uniform Acceleration

also linear acceleration, particularly gravitation

A body under uniform acceleration a changes its velocity v steadily during the time t:

v = a · t

The traveled distance s is increasing quadraticly with time.

s = a / 2 · t ²

A particular case is the free fall of a body.

In this case the acceleration is

1 g = 9,81 m/s² (g like gravitation).

### Newton's Law

When a body with the mass m is accelerated with an acceleration a then the force F is acting on the body.

F = m · a

The dimension of a force is called Newton [N].

1 Newton [N] is the force that accelerates 1 kg

mass with 1m/s²

or

If a body with1 kg mass is accelerated with 1m/s²

then a force of 1 Newton [N] is acting on that body.

1 N equals about to the weight of a regular chocolate bar of 100gr.

### Alternating Acceleration

The motion of a mass attached to a spring presents a particular case where the acceleration changes its magnitude and direction periodically.

When the mass is lifted and left to itself it oscillates on the resonance frequency of the system.