# Dsp00100-periodic motion and sinusoids

 Page 2 / 7

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.

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
Got questions? Join the online conversation and get instant answers!