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Math Help - Period of the sum of two cosines

  1. #1
    Newbie sjcomp's Avatar
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    Period of the sum of two cosines

    Hello,

    I remember that if I sum two cosine waves the period of the resulting function will be extended. How do I find this new period? I also remember that if the ratio of the periods satisfies a condition then the period never repeats. I do not remember what the condition is. Or maybe it should be a multiplication and not a sum... Can someone remind me about this?

    Thanks a lot.
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by sjcomp View Post
    Hello,

    I remember that if I sum two cosine waves the period of the resulting function will be extended. How do I find this new period? I also remember that if the ratio of the periods satisfies a condition then the period never repeats. I do not remember what the condition is. Or maybe it should be a multiplication and not a sum... Can someone remind me about this?

    Thanks a lot.
    In general, the period would be the least common multiple of the two periods you have been given.

    For example : period pi/2 and period pi/3.

    2*pi/2=pi
    3*pi/2=3pi/2
    4*pi/2=2pi
    .
    .
    .
    ----------
    2*pi/3=2pi/3
    3*pi/3=pi
    4*pi/3=4pi/3
    .
    .
    .


    Period is pi

    If you give an example, I think I'll be able to explain better
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  3. #3
    Newbie sjcomp's Avatar
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    Thanks, Moo. I see it's the same method as your reply to my other question Do you know anything about my second question if there is a relationship between the summed periods that would not result in a common multiple?

    Thanks.
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