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A Periodic Function Looks Like This Formula?

  1. Mar 7, 2016 #1
    My book says this:

    upload_2016-3-7_19-17-13.png

    I don't understand how this works. I learned that the usual sunisoidal function looks like
    sin(wt+phi), where w is frequency, t is time, and phi is some offset.

    EQ 17.1 doesn't match the bolded formula above. How does this work?
     
  2. jcsd
  3. Mar 7, 2016 #2

    anorlunda

    Staff: Mentor

    They are talking about periodic functions that are not necessarily sinusoidal. A square wave for example,
     
  4. Mar 8, 2016 #3

    Tom.G

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    Science Advisor

    f(t) = f(t + nT)

    Where 0 <= T < infinity the period of one cycle
    0 <= t < T the time interval between samples within a cycle
    n=0 1 2 3... which cycle you are evaluating

    Looking at the RHS, the part f(t) would be one cycle of a waveform
    and the full RHS, f(t + nT) is the waveform of the n th cycle.

    All that is saying is that f(t) stays the same regardless of which cycle you look at, which is the definition of a periodic function.

    phi isn't used here because the waveform is assumed to start at zero phase, and (t) can be any function of t , such as wt .
     
  5. Mar 8, 2016 #4

    PeroK

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    Science Advisor
    Homework Helper
    Gold Member

    Yes, it does match.

    Let ##f(t) = sin(wt + \phi)##

    Then ##f(t) = f(t + nT)##, where ##T = 2\pi / \omega##
     
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