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Periodic function | Change of variables

  1. Nov 6, 2009 #1
    "Is f(x)=sin(x2) periodic?
    Answer: no."


    WHY? I believe "sin" is always periodic? Can someone please explain?


    Any help is appreciated!
     
    Last edited: Nov 7, 2009
  2. jcsd
  3. Nov 6, 2009 #2

    berkeman

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    Staff: Mentor

    On the first one, what is the definition of periodic? And when you have a non-linear argument to the sin() funtion, what is the period?
     
  4. Nov 6, 2009 #3

    HallsofIvy

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    Staff Emeritus
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    If x= 0, [itex]sin(x^2)= sin(0^2)= sin(0)= 0[/itex]. When is [itex]sin(x^2)= 0[/itex] again? Is that a period?
     
  5. Nov 7, 2009 #4
    I know that f(x)=sin(x) has period 2pi, g(x)=sin(2x) has period pi, etc. Since I am seeing sin in the function sin(x^2), this leads me to think that sin(x^2) is periodic as well.

    For sin(x^2), The zero set is {x: x^2 = (n)(pi)}, but how can I know whether it's periodic or not?
    I think it's hard for me to tell whether a function given randomly to me is periodic or not. Is there any systematic way to answer this? I am not sure where to start...

    Thanks!
     
  6. Nov 7, 2009 #5
    For sin(x^2), The zero set is {x: x^2 = (n)(pi)}, but how can I know whether it's periodic or not? I just can't tell...
     
  7. Nov 7, 2009 #6

    lanedance

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    periodic in my book would be
    f(t+a) = f(t) for all t, for som constant a

    in your case, solve for the first few zeros, and see what the difference bewteen them is (cf with a in the above) , see if there's any pattern which you can pick out which shows its not periodic
     
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