A function that repeats itself after a specific period of time is called a Periodic Function. More about Periodic Function
For a periodic function g(x) with period a, g(x + a) = g(x). The trigonometric Functions, such as sine and cosecant are periodic functions with period 2π, and tangent is a periodic function with period π. Examples of Periodic Function
The hands of a clock show periodic behavior with time as variable. The seasons in year show a periodic behavior. Solved Example on Periodic Function
Identify the graph that does not represent a periodic function.
This particular example is a real recording of a real person humming and the repetition is not perfect. This is often the case with real data. In theory, for example, a spring-and-mass system should oscillate like a perfect sine function but in practice imperfections in the experimental set up often change the results a bit.
The four graphs below show several additional examples. All four of these examples have period 3. The first two are particularly relevant for the study of Nancy's blown speaker. The left graph shows a very pure tone of period 3. The right graph shows the same signal after clipping. Notice it still has period 3. Clipping a signal doesn't change the period but it does change the signal in other ways. It is these other changes that caused Nancy's speaker to blow out. The tools that we develop in this module will enable us to understand exactly why Nancy's speaker blew out. {http://www.math.montana.edu/frankw/ccp/multiworld/virtual/FourSer/body.htm}
For math, a periodic function repeats itself in intervals over a period of time. A trigonometric function repeats itself over a period of 2pi. A periodic function can be used in real life to describe waves.
When you are measuring waves, you also use a wavelength. A wavelength is the distance between crests or troughs in a wave that are consecutive. Say your length is t and the function is f; if the value of the function would be x + t is equal to x at the function value, f is a periodic function. The period in a graph is the shortest length that t repeats. The highest value in the function is called the amplitude. These can all be shown on a graph.
For example, if you would draw a graph of a wave, on the coordinate plane you would chart the lowest point of the wave and the highest point as it keeps going up and down. Each time it goes up and down, it starts a new periodic function.
This is what we learned in class this week on section 8, but we just tied it into real life waves. You can use many different objects in real life to graph periodic functions.
A periodic function is a function that has a graph that repeats itself exactly like itself over and over as it goes from left to right. http://www.mathwords.com/p/periodic_function.htm
The periodic function written in standard form is f(x + t) = f (x). A period of the function is the shortest length t can be. The frequency of a function is how many times a number will repeat itself within a certain time or fixed space.
When graphing functions if two of them have the same period and the frequency repeats at different values of independent variables are called the phase angle.
Repeating patterns of waves happen in the real world. Sound is an example of something traveling in waves. Energy transmits liquids on the surface in the form of waves, radio signals and the changing current of electricity act likes waves too. Light not only behaves like a wave but a particle as well.
Periodic functions are functions that repeat over and over, or cycle on a specific period. The most important examples are the trigonometric functions, which repeat over intervals of 2pi. A function that is not periodic is known as aperiodic.
A property of some periodic functions that cycle within some definite range is that they have an amplitude in addition to a period. The amplitude of a periodic function is the distance between the highest point and the lowest point, divided by two.
A function is considered periodic if f(x+p)=f(x) for all values of x. A function with period P will repeat on intervals of length P.
Everyday examples are seen when the variable is time. For example, the hands on the clock or the phases of the moon show periodic behavior. Also, sound travels in waves, energy changes propagate on the surfaces of liquids in the form of waves, radio signals travel as waves, and alternating current electricity behaves like a wave. All these are considered to behave like periodic functions since they repeat over and over.
A periodic function is a function who's values repeat at regular intervals. For example, and interval of length (t), and a function (f), if the value at the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this it is written f(x + t)=f(x).
The repetition of a periodic function can be compared to the repetition of wave patterns. For instance on a graph where the line repeats itself many times when displaying information. Another example of this is sound. Sound travels in lots of repetitious waves. Light also travels in lots of repetitious waves. Radio signals, cell phone signals, etc. all use waves.
We use periodic functions in many hidden ways in life. These are just a few ways that we use periodic functions.
A periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.
The trigonometric functions sine and cosine are common periodic functions, with period 2π. The subject of Fourier series investigates the idea that a periodic function is a sum of trigonometric functions with matching periods.
Ex.For example, the sine function is periodic with period 2π, since sin(x+2pi)=sin(x) for all values of x. This function repeats on intervals of length 2π
A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle. http://science.jrank.org/pages/5098/Periodic-Functions.html
This is applicable to everything today that has to do with waves. These formulas could be used to measure the frequencys of radio waves or even to measure something like interest at the bank.
A periodic function repeats itself in intervals over a period of time. A trigonometric function repeats itself over a period of 2pi. A periodic function can be used in real life to describe waves. When you are measuring waves, you also use a wavelength. A wavelength is the distance between crests or troughs in a wave that are consecutive.
When your length is t and the function is f; if the value of the function would be x + t is equal to x at the function value, f is a periodic function. The period in a graph is the shortest length that t repeats. The highest value in the function is called the amplitude.
For example, repeating patterns of waves happen in the real world. Sound is an example of something traveling in waves. Energy transmits liquids on the surface in the form of waves, radio signals and the changing current of electricity act likes waves too. Light not only behaves like a wave but a particle as well.
A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle.
The way a periodic function can be used in many different ways in real life. Things such as sun rise and sun set, the tide, seasons, and other such things are just a few examples.
In mathematics, a period is a function that repeats itself in intervals or regular patterns. What is most important about periods, is its function in the field of trigonometry. In trigonometry, periods are intervals of over length 2π.
A function is considered a period if:
F(x + P) = F(x)
The variable P, is the period, and it never equals zero.
In our everyday world, periods are used in many fields. Periods are used through the fields of science to describe waves, oscillations, and there are many other types of occurrences of periods.
Examples of periods:
Sound waves and radio waves Tides and how the moon affects the water waves. Daily noontime air pressure Light waves travel at certain wavelengths Radar is designed to pulsate at set amplitudes and speeds.
As we become more aware of functions such as periods, we will begin to realize how important mathematics is in our lives and how applicable it is to certain cases.
Periodic functions are functions that repeat over and over on a specific period. Standard function notation is written as f(x+t)=f(x). The shortest length on a graph is called the period. Sin and cos are periodic functions with a period of 2pi. Tangent has a period of pi. There are two ways to classify a model, either cyclical or period bahvior.
In today's world periodic functions can be used for many things including temperatures, things in the business world, and even the hands on a clock. Waves are periodic functions including sound waves. They repeat themselves over a period of time. The currents of electricity are waves too. Light can even act like a wave but its also a particle. http://science.jrank.org/pages/5098/Periodic-Functions.html
All graphs can vary and range anywhere from fluid flow, wave motion, tides, AC currents, etc. http://www.usna.edu/MathDept/website/courses/calc_labs/sinecurve/Application.html
Something that repeats itself in intervals over a period of time is a periodic function in math. A periodic function can be put into use in real life to describe waves. When put into a trigonometric function it repeats itself over a period of 2π.
To measure waves, we use wavelength as well. A wavelength is the distance between crests, also known as troughs, in a wave that are consecutive. Say your length is b and the function is f; if the value of the function would be x + b is equal to x at the function value, f is a periodic function. The shortest length that b repeats on the graph is the period. The highest value in the function is called the amplitude. All can be shown on a graph.
For example, graph a wave, on a coordinate plane and chart the lowest point of the wave and the highest point and you’ll see how it keeps going up and down. Each time it goes up and down, it starts a new periodic function.
We learned this in Chapter 8 this week. The difference is we just tied it into real life waves. You can use this in real life to graph periodic functions.
A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle.
F(x + P) = F(x)
The variable P, is the period, and it never equals zero.
In our everyday world, periods are used in many fields. Periods are used through the fields of science to describe waves, oscillations, and there are many other types of occurrences of periods.
A periodic function is a function, usually on a graph, that repeats itself over and over again in a given period of time. The occurrences happen at regular intervals. In chapter eight this week we learned that periodic functions measure how or when a wave repeated itself. Sine and cosine have periodic functions. We also learned that in order to to find the period of them you have to use the formula 2pi/ b.
All information can be found from looking at graphs of functions or given equations.
Ex. In 3 sin 4x The A is 3. The B is 4. The formula is 2pi/B which means 2(180)/4 In radians the period is said to be pi/4 or 90 in degrees.
Periodic functions are used everyday in various fields. They are mostly used to describe waves. Some fields are : Describing radio and sound waves. Understanding XRays Tidesn high & low. In hospitals ( heart monitors) Describing light waves And sound waves.
Periodic functions are not only important in mathematics, but they also help people in the real world every day.
Periodic Function
ReplyDeleteDefinition of Periodic Function
A function that repeats itself after a specific period of time is called a Periodic Function.
More about Periodic Function
For a periodic function g(x) with period a, g(x + a) = g(x).
The trigonometric Functions, such as sine and cosecant are periodic functions with period 2π, and tangent is a periodic function with period π.
Examples of Periodic Function
The hands of a clock show periodic behavior with time as variable.
The seasons in year show a periodic behavior.
Solved Example on Periodic Function
Identify the graph that does not represent a periodic function.
Related Terms for Periodic Function
Function
Period
Time
Trigonometric Functions
{http://www.icoachmath.com/SiteMap/Periodic_Function.html}
This particular example is a real recording of a real person humming and the repetition is not perfect. This is often the case with real data. In theory, for example, a spring-and-mass system should oscillate like a perfect sine function but in practice imperfections in the experimental set up often change the results a bit.
The four graphs below show several additional examples. All four of these examples have period 3. The first two are particularly relevant for the study of Nancy's blown speaker. The left graph shows a very pure tone of period 3. The right graph shows the same signal after clipping. Notice it still has period 3. Clipping a signal doesn't change the period but it does change the signal in other ways. It is these other changes that caused Nancy's speaker to blow out. The tools that we develop in this module will enable us to understand exactly why Nancy's speaker blew out.
{http://www.math.montana.edu/frankw/ccp/multiworld/virtual/FourSer/body.htm}
This comment has been removed by the author.
ReplyDeleteFor math, a periodic function repeats itself in intervals over a period of time. A trigonometric function repeats itself over a period of 2pi. A periodic function can be used in real life to describe waves.
ReplyDeleteWhen you are measuring waves, you also use a wavelength. A wavelength is the distance between crests or troughs in a wave that are consecutive. Say your length is t and the function is f; if the value of the function would be x + t is equal to x at the function value, f is a periodic function. The period in a graph is the shortest length that t repeats. The highest value in the function is called the amplitude. These can all be shown on a graph.
For example, if you would draw a graph of a wave, on the coordinate plane you would chart the lowest point of the wave and the highest point as it keeps going up and down. Each time it goes up and down, it starts a new periodic function.
This is what we learned in class this week on section 8, but we just tied it into real life waves. You can use many different objects in real life to graph periodic functions.
http://science.jrank.org/pages/5098/Periodic-Functions.html
A periodic function is a function that has a graph that repeats itself exactly like itself over and over as it goes from left to right.
ReplyDeletehttp://www.mathwords.com/p/periodic_function.htm
The periodic function written in standard form is f(x + t) = f (x). A period of the function is the shortest length t can be. The frequency of a function is how many times a number will repeat itself within a certain time or fixed space.
When graphing functions if two of them have the same period and the frequency repeats at different values of independent variables are called the phase angle.
Repeating patterns of waves happen in the real world. Sound is an example of something traveling in waves. Energy transmits liquids on the surface in the form of waves, radio signals and the changing current of electricity act likes waves too. Light not only behaves like a wave but a particle as well.
http://science.jrank.org/pages/5098/Periodic-Functions.html
Periodic functions are functions that repeat over and over, or cycle on a specific period. The most important examples are the trigonometric functions, which repeat over intervals of 2pi. A function that is not periodic is known as aperiodic.
ReplyDeleteA property of some periodic functions that cycle within some definite range is that they have an amplitude in addition to a period. The amplitude of a periodic function is the distance between the highest point and the lowest point, divided by two.
A function is considered periodic if
f(x+p)=f(x)
for all values of x. A function with period P will repeat on intervals of length P.
Everyday examples are seen when the variable is time. For example, the hands on the clock or the phases of the moon show periodic behavior. Also, sound travels in waves, energy changes propagate on the surfaces of liquids in the form of waves, radio signals travel as waves, and alternating current electricity behaves like a wave. All these are considered to behave like periodic functions since they repeat over and over.
http://science.jrank.org/pages/5098/Periodic-Functions.html
http://en.wikipedia.org/wiki/Periodic_function
A periodic function is a function who's values repeat at regular intervals. For example, and interval of length (t), and a function (f), if the value at the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this it is written f(x + t)=f(x).
ReplyDeleteThe repetition of a periodic function can be compared to the repetition of wave patterns. For instance on a graph where the line repeats itself many times when displaying information. Another example of this is sound. Sound travels in lots of repetitious waves. Light also travels in lots of repetitious waves. Radio signals, cell phone signals, etc. all use waves.
We use periodic functions in many hidden ways in life. These are just a few ways that we use periodic functions.
http://science.jrank.org/pages/5098/Periodic-Functions.html
A periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.
ReplyDeleteThe trigonometric functions sine and cosine are common periodic functions, with period 2π. The subject of Fourier series investigates the idea that a periodic function is a sum of trigonometric functions with matching periods.
Ex.For example, the sine function is periodic with period 2π, since
sin(x+2pi)=sin(x)
for all values of x. This function repeats on intervals of length 2π
http://answers.com/topic/periodic-function
A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle.
ReplyDeletehttp://science.jrank.org/pages/5098/Periodic-Functions.html
This is applicable to everything today that has to do with waves. These formulas could be used to measure the frequencys of radio waves or even to measure something like interest at the bank.
A periodic function repeats itself in intervals over a period of time. A trigonometric function repeats itself over a period of 2pi. A periodic function can be used in real life to describe waves. When you are measuring waves, you also use a wavelength. A wavelength is the distance between crests or troughs in a wave that are consecutive.
ReplyDeleteWhen your length is t and the function is f; if the value of the function would be x + t is equal to x at the function value, f is a periodic function. The period in a graph is the shortest length that t repeats. The highest value in the function is called the amplitude.
For example, repeating patterns of waves happen in the real world. Sound is an example of something traveling in waves. Energy transmits liquids on the surface in the form of waves, radio signals and the changing current of electricity act likes waves too. Light not only behaves like a wave but a particle as well.
http://en.wikipedia.org/wiki/Periodic_function
A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle.
ReplyDeletehttp://science.jrank.org/pages/5098/Periodic-Functions.html
The way a periodic function can be used in many different ways in real life. Things such as sun rise and sun set, the tide, seasons, and other such things are just a few examples.
http://answers.yahoo.com/question/index?qid=20100218175226AAmhy08
In mathematics, a period is a function that repeats itself in intervals or regular patterns. What is most important about periods, is its function in the field of trigonometry. In trigonometry, periods are intervals of over
ReplyDeletelength 2π.
A function is considered a period if:
F(x + P) = F(x)
The variable P, is the period, and it never equals zero.
In our everyday world, periods are used in many fields. Periods are used through the fields of science to describe waves, oscillations, and there are many other types of occurrences of periods.
Examples of periods:
Sound waves and radio waves
Tides and how the moon affects the water waves.
Daily noontime air pressure
Light waves travel at certain wavelengths
Radar is designed to pulsate at set amplitudes and speeds.
As we become more aware of functions such as periods, we will begin to realize how important mathematics is in our lives and how applicable it is to certain cases.
http://answers.yahoo.com/question/index;_ylt=Ah4AjR9BkfX3IeJcXKWx44wjzKIX;_ylv=3?qid=20090211184622AAT84Gi
http://answers.yahoo.com/question/index;_ylt=AhgguZ9vGtPgqDy9gLN6wGIjzKIX;_ylv=3?qid=20090421092057AAGRPoC
Periodic functions are functions that repeat over and over on a specific period. Standard function notation is written as f(x+t)=f(x). The shortest length on a graph is called the period. Sin and cos are periodic functions with a period of 2pi. Tangent has a period of pi. There are two ways to classify a model, either cyclical or period bahvior.
ReplyDeleteIn today's world periodic functions can be used for many things including temperatures, things in the business world, and even the hands on a clock. Waves are periodic functions including sound waves. They repeat themselves over a period of time. The currents of electricity are waves too. Light can even act like a wave but its also a particle.
http://science.jrank.org/pages/5098/Periodic-Functions.html
All graphs can vary and range anywhere from fluid flow, wave motion, tides, AC currents, etc.
http://www.usna.edu/MathDept/website/courses/calc_labs/sinecurve/Application.html
Something that repeats itself in intervals over a period of time is a periodic function in math. A periodic function can be put into use in real life to describe waves. When put into a trigonometric function it repeats itself over a period of 2π.
ReplyDeleteTo measure waves, we use wavelength as well. A wavelength is the distance between crests, also known as troughs, in a wave that are consecutive. Say your length is b and the function is f; if the value of the function would be x + b is equal to x at the function value, f is a periodic function. The shortest length that b repeats on the graph is the period. The highest value in the function is called the amplitude. All can be shown on a graph.
For example, graph a wave, on a coordinate plane and chart the lowest point of the wave and the highest point and you’ll see how it keeps going up and down. Each time it goes up and down, it starts a new periodic function.
We learned this in Chapter 8 this week. The difference is we just tied it into real life waves. You can use this in real life to graph periodic functions.
http://science.jrank.org/pages/5098/Periodic-Functions.html
A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle.
ReplyDeleteF(x + P) = F(x)
The variable P, is the period, and it never equals zero.
In our everyday world, periods are used in many fields. Periods are used through the fields of science to describe waves, oscillations, and there are many other types of occurrences of periods.
A periodic function is a function, usually on a graph, that repeats itself over and over again in a given period of time. The occurrences happen at regular intervals. In chapter eight this week we learned that periodic functions measure how or when a wave repeated itself. Sine and cosine have periodic functions. We also learned that in order to to find the period of them you have to use the formula 2pi/ b.
ReplyDeleteAll information can be found from looking at graphs of functions or given equations.
Ex. In 3 sin 4x
The A is 3. The B is 4.
The formula is 2pi/B which means 2(180)/4
In radians the period is said to be pi/4 or 90 in degrees.
Periodic functions are used everyday in various fields. They are mostly used to describe waves. Some fields are :
Describing radio and sound waves.
Understanding XRays
Tidesn high & low.
In hospitals ( heart monitors)
Describing light waves
And sound waves.
Periodic functions are not only important in mathematics, but they also help people in the real world every day.