5

I have a question about analyzing the data from a coupled pendulum.

I have measured the amplitude $\psi(t)$ which is expected to be a beat and I want to measure the period. The ideal plot would be something like this.

enter image description here

I have to measure the period of the envelope and the individual components.

The image is ideal, because the amplitude will be decreasing slowly with time.

So I would like to know the best method to calculate the period and its error. I have considered these options:

  • Fast Fourier Transform (FFT): The problem I see is that it's not a totally periodic function, so it might introduce more error. And I've read that the error is related to the covariance matrix, but I don't understand it.

  • Measuring the distance between maxima/minimum: This would not be affected by the damping, but you would waste many points.

Scortchi - Reinstate Monica
  • 27,560
  • 8
  • 81
  • 248
jinawee
  • 150
  • 6
  • 1
    I feel that my question is not very good. Would it be better for Signal Processing? Is it too broad or too physics related? – jinawee Feb 19 '14 at 00:21
  • 3
    Your question is answered (in different ways!) at http://stats.stackexchange.com/questions/16230 and at http://stats.stackexchange.com/questions/16117. It is not possible to say which is "best" without knowing more about the kinds of errors you might incur and what decisions you will be making based on the resulting estimate. I have not voted to close this thread, though, because you ask a novel follow-on question: how to estimate the error in the calculation. I don't think that has been adequately addressed here before. We could do a good job with some more info about your errors. – whuber Feb 19 '14 at 00:21
  • I think that the approach described [here](http://stats.stackexchange.com/questions/60994/fit-a-sinusoidal-term-to-data/60997#60997) with `nls` could provide an estimate of the uncertainty/error involved. (The answers mainly focus on getting good starting values, but `nls` should estimate the error and you should be able to pull it out with `vcov`). – David J. Harris Feb 19 '14 at 05:10

0 Answers0