Spring Mass Fourier Transform Analogy

Fourier transform converts an amplitude over time data set
into an amplitude over frequency data set. An example of its
application is the equalizer in a sound system. The equalizer takes a
sample of the sound and converts it into an amplitude over frequency
bar graph. Every sample of an analog wave form can be broken down
into a set of sine waves. It is even possible to make something as
complex as a square wave by combining multiple sine waves together.
There are many mathematical models and algorithms to accomplish
this task, however there aren’t many mechanical analogies for the
process.
Using a mechanical analogy Fourier transform can be accomplished
by setting up a row of tuning forks which pick up sound from a piano
as seen in Figure 1. You can set up a tuning fork for each note which
will resonate with the music. When you press the C key, the tuning fork
which resonates with the C key will begin to vibrate while the others
are at a stand still.
In order to simulate a tuning fork inside of a computer program, the
software engineer must create a model which works the same way. The
best and most simple method is to simulate a spring-mass system which
also has the property of having a mechanical resonance and behaves the
same way as a tuning fork. In Figure 2, you can see a model of a
springmass tuning fork analogy. Using Hooke's law and a particle
simulation, you will have all the elements necessary to make the simulation
work. Each spring-mass element will be fed an analog signal
and will resonate if it is exposed to a sine wave component which
matches it. Amplitude over frequency can be established by measuring
the average sinusoidal velocity of the mass connected to the spring
which then is used as the output of the transform.