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Math Help - A function that is naturally periodic?

  1. #1
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    A function that is naturally periodic?

    ok guys, im having trouble with this problem
    this is due very soon

    this was the question given

    Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

    Identify the period.

    Graph the function.

    what does it mean by naturally periodic? maybe i can do it if i know what it means, also how do i figure out a period of a regular function? i only know how to do it to trig functions

    any help is appreciated, thanks
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  2. #2
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    Quote Originally Posted by ruthvik View Post
    Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).
    Use the floor function: f(x) = x - \left\lfloor x \right\rfloor
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  3. #3
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    Quote Originally Posted by ruthvik View Post
    ok guys, im having trouble with this problem
    this is due very soon

    this was the question given

    Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

    Identify the period.

    Graph the function.

    what does it mean by naturally periodic? maybe i can do it if i know what it means, also how do i figure out a period of a regular function? i only know how to do it to trig functions

    any help is appreciated, thanks
    A function that is naturally periodic is any function based on a cyclical variable. One good "natural" cyclical variable is clock time. You can set up a simple equation with time as the variable, like y = 2t, and they graph the equation with t as the horizontal axis.
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  4. #4
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    Quote Originally Posted by sinewave85 View Post
    A function that is naturally periodic is any function based on a cyclical variable. One good "natural" cyclical variable is clock time. You can set up a simple equation with time as the variable, like y = 2t, and they graph the equation with t as the horizontal axis.
    i dont understand what cyclical variables are

    also, i dont know what that equation the other guy made, i can graph it but im thinking of this answer in more simple terms
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  5. #5
    Member sinewave85's Avatar
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    Quote Originally Posted by ruthvik View Post
    i dont understand what cyclical variables are

    also, i dont know what that equation the other guy made, i can graph it but im thinking of this answer in more simple terms

    Sorry, the answer I gave won't work because it it not a function -- it wont pass the vertical line test. I am trying to think of a way to construct a simple periodic function -- one the oscillates up and down -- without using a sin function.
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  6. #6
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    What do you not like about my function? It has a natural period of 1.
    Attached Thumbnails Attached Thumbnails A function that is naturally periodic?-floor.gif  
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  7. #7
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    Quote Originally Posted by Plato View Post
    What do you not like about my function? It has a natural period of 1.
    i never learned that function, so i cannot use it, otherwise i would have : D

    thanks though
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  8. #8
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    Quote Originally Posted by ruthvik View Post
    i never learned that function, so i cannot use it, otherwise i would have.
    You mean that you never learned the greatest integer function?
    The floor function is just a more modern notation for that.
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  9. #9
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    Quote Originally Posted by Plato View Post
    You mean that you never learned the greatest integer function?
    The floor function is just a more modern notation for that.
    oh wow?? really? i learned GINT, but tell me plato, if my teacher asks how i got this, how will i explain to him? how can i graph this on paper? because i only learned what it is , will it work if i use plug in for x and stuff?
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  10. #10
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    For every x, \left\lfloor x \right\rfloor  \leqslant x < \left\lfloor x \right\rfloor  + 1\; \Rightarrow \;0 \leqslant x - \left\lfloor x \right\rfloor  < 1.

    As you can see the graph goes from 0 to 1 (never equal to 1) between any two consecutive integers.
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  11. #11
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    Quote Originally Posted by Plato View Post
    For every x, \left\lfloor x \right\rfloor  \leqslant x < \left\lfloor x \right\rfloor  + 1\; \Rightarrow \;0 \leqslant x - \left\lfloor x \right\rfloor  < 1.

    As you can see the graph goes from 0 to 1 (never equal to 1) between any two consecutive integers.
    this might be a stupid question but when i graph it, there is a open circle on the top part right? like (1,1)

    thanks btw, your eq was a good example
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  12. #12
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    Quote Originally Posted by ruthvik View Post
    this might be a stupid question but when i graph it, there is a open circle on the top part right? like (1,1)

    thanks btw, your eq was a good example
    yes
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