# Dsp00100-periodic motion and sinusoids

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I will show you examples of using composition to create a square waveform and a triangular waveform.

I will identify some real-world examples of frequency filtering and real-time spectral analysis

## Periodic motion

The most difficult decision that I must make for this series is to decide where to begin. I need to begin at a sufficiently elementary level that you willunderstand everything that you read. So, before getting into the actual topic of digital signal processing, I'm going to take you back to some elementary physicsand mathematical concepts and discuss periodic motion .

Many physical devices (and electronic circuits as well) exhibit a characteristic commonly referred to as periodic motion. This includes pendulums,acoustic speakers, springs, human vocal cords, etc.

## Motion of a pendulum

For example, consider the pendulum on a grandfather clock. Once you start the pendulum swinging, it will swing for a long time (actually, the spring in the clock gives it a little kick during each repetition, so it will continue toswing until the spring runs down).

The most important characteristic of the motion of the pendulum is that every repetition takes almost exactly the same amount of time. In other words, theperiod of time during which the pendulum swings from one side to the other is very constant. That is the source of the term periodic motion .

## A bag of sand

Even without the spring to help it along, a pendulum swinging in a low-friction environment will swing for a long time. Visualize a pendulumconsisting of a bag of sand tied to the end of a long rope suspended from your ceiling (sheltered from the wind). Assume that the bag is filled with colored sand, and that it has a small hole in the bottom. Assume that you startit swinging in a back-and-forth motion (no circular motion).

## The sand traces out a pattern

As the bag of sand swings back and forth, a little bit of sand will leak out of the hole and land on the floor below. The sand will trace out a line, whichis parallel to the direction of motion of the bag of sand.

Now assume that you carefully drag a carpet across the floor under the bag at a uniform rate, perpendicular to the direction of motion of the bag. This willcause the sand that leaks from the bag to trace out a zigzag pattern on the carpet very similar to the curved line shown in Figure 1 .

Figure 1. A sinusoidal function.

## A sinusoidal function

The shape of the curve shown in Figure 1 is often referred to as a sinusoidal function.

In this assumed scenario, the bag is swinging back and forth along the vertical axis in Figure 1 , and the carpet is being dragged along the horizontal axis. The motion of the bag causes the sand to be leaked in a back-and-forthzigzag pattern. The motion of the carpet causes that pattern to be elongated along the horizontal axis.

A sinusoidal function:

Figure 1 is a plot of the following Java expression:

`Math.cos(2*pi*x/50) + Math.sin(2*pi*x/50)`

Math in the above expression is the name of a Java library that provides methods for computing sine, cosine, andvarious other mathematical functions.

The asterisk (*) in the above expression means multiplication.

The reference to pi in the above expression is a reference to the mathematical constant with the same name.

The image in Figure 1 was produced using a Java program named Graph03 , which I will describe in a future module.

what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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