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How to tell if two oscillators are different

  1. Mar 31, 2013 #1
    Hi all, this is my first time on PF. As one of my projects, I had to create a program to analyze a bunch of data involving oscillators. I'm supposed to find out how many different oscillators there are within all the data. I have it pretty much done, except one part. I don't actually know how to tell if two oscillators are the same or different.

    The equations I'm supposed to use are:
    x(t) = x_max cos(ωt + [itex]\phi[/itex])
    v(t) = -ω x_max sin(ωt + [itex]\phi[/itex])
    a(t) = -ω^2 x_max cos(ωt + [itex]\phi[/itex])

    I'm given t, x, v, and a. I have managed to calculate all x_max, ω and [itex]\phi[/itex] value.

    Basically what my questions are:
    How do I know if two oscillators are the same or different?
    If they have the same x_max value and ω value, but different [itex]\phi[/itex] value, are they still the same oscillator?

    Thanks all
  2. jcsd
  3. Mar 31, 2013 #2


    User Avatar

    Staff: Mentor

    Hi fallenshadow95, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    In general, taking the output of an oscillator and phase-shifting is not regarded as creating a second independent oscillator. But in the application where your data originates, their interpretation may differ.

    I think you need to ask your lecturer to clarify this point if it will arise in what you are doing.
    Last edited by a moderator: May 6, 2017
  4. Apr 1, 2013 #3
    It is mathematically impossible to distinguish how many phase shifted sine signals of the same frequency are superimposed. The sum of any number of these is still a single sine signal.
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