- #1

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I know that its possible to use f(x) = f(x+T), while T is the period frequency.

But how to find out T ? and how to contradict this equation to say that the function is not periodic.

Thanks, gafar.

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In summary, the conversation discusses whether the function sin(x^2) is periodic. Gafar wants to prove that it is not periodic, but is unsure how to do so. Mikey suggests plotting the function and Rajini provides plots for three different ranges of x values. However, Willem2 points out that the function cannot have a period of 0, making it not periodic. The conversation also touches on the definition of a periodic function and the possibility of using a mathematical proof to show that sin(x^2) is not periodic.

- #1

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I know that its possible to use f(x) = f(x+T), while T is the period frequency.

But how to find out T ? and how to contradict this equation to say that the function is not periodic.

Thanks, gafar.

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- #2

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Hi gafar,

i quickly plot your function f(x)=sin(x*x).

between three x ranges [see figures below]

1. between -10 to 10,

2. -100 to 100 and

3. -1000 to 1000.

from that it follows a kind of periodic change. [in general most of the sin functions are periodic]

i quickly plot your function f(x)=sin(x*x).

between three x ranges [see figures below]

1. between -10 to 10,

2. -100 to 100 and

3. -1000 to 1000.

from that it follows a kind of periodic change. [in general most of the sin functions are periodic]

Last edited:

- #3

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- #4

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Rajini said:Hi gafar,

i quickly plot your function f(x)=sin(x*x).

between three x ranges [see figures below]

1. between -10 to 10,

2. -100 to 100 and

3. -1000 to 1000.

from that it follows a kind of periodic change. [in general most of the sin functions are periodic]

Thanks, still waiting for your pics to be approved. So just to be sure, when you see periodic changes it means that the function is NOT periodic right?

And I know that its easy to conclude the answer from a plot but is there an simple arithmetic proof?

and thanks a lot.!

- #5

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assume it is periodic...

for the function to be periodic with period T, y(x) = y(x+T)

but also as we know y is continuous, y'(T) = y'(x+T) (same gradient for it to be periodic)

ie.

sin(x^2) = sin(x^2 + 2xT + T^2)

2x*sin(x^2) = (2x+2T)sin(^2 + 2xT + T^2)

divide bottom by the top:

2x = (2x+2T)

T = 0

ie. it is not periodic!

- #6

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When a function changes periodically, that means the function is periodic.

Your function to me is some kind of periodic motion, but not just noise!

There are many types of periodic motion..simplest one is sin(x) function..

If a function is not periodic= probably should be noise..

Sorry i am not good in mathematical proof..however, someone will help you..

good luck

- #7

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i notice some typing error..

will it is like this:

[tex]\sin (x^2)=\sin(x^2+2xT+T^2)[/tex]

[tex]2x\cos(x^2)=2(x+T)\cos(x^2+T^2+2xT)[/tex]??

- #8

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Oh god. I am not on the ball today. Sorry.

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- #10

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Please prove some details..where you want to use sin(x*x)?? etc..

As mikey said:

if T is same then it is periodic..otherwise not..Remember sine wave in which the period is same, i.e. the wavelength is same..so sine wave is periodic..

[why no reply from experts?]

- #11

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gafar said:

There's a definition of a periodic function. Who uses the definition and who has just

plotted it and said that it looks periodic?

The proof by Mikey is incomplete however.

It can be made to work if you substitute x = 0. You get

[itex] \sin {(T^2)} = 0 [/itex]

[itex] 2 T \cos {(T^2)} = 0 [/itex]

Since sin(x) and cos(x) are never both 0, these equations can only be both fulfilled

if T = 0

- #12

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so sin(x*x) is periodic if T is not equal to zero!

is that correct?

I am just asking out of curiosity.

thanks

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- #14

Homework Helper

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Rajini said:Hi gafar,

i quickly plot your function f(x)=sin(x*x).

between three x ranges [see figures below]

1. between -10 to 10,

2. -100 to 100 and

3. -1000 to 1000.

Rajini the function y=sin(x

- #15

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I made those plots using gnuplot.

If that function is periodic then the period should be extremely small!

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