How to tell if two oscillators are different

[fallenshadow95]

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 + \phi)
v(t) = -ω x_max sin(ωt + \phi)
a(t) = -ω^2 x_max cos(ωt + \phi)

I'm given t, x, v, and a. I have managed to calculate all x_max, ω and \phi 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 \phi value, are they still the same oscillator?

Thanks all

 

[NascentOxygen]

If they have the same x_max value and ω value, but different \phi value, are they still the same oscillator?

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

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.

 

[0xDEADBEEF]

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.