# 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.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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