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How do I fit a damped sine wave to data

For my experimental project I have fit a damped sine wave onto data I acquired for the amplitude of vibration. I am trying to analyse the data in python but don't even know where to start when trying to model it as a damped wave. So any tips or help on how to get started would be much appreciated.

The Amplitude data is as follows:

A = [174, 174, 173, 173, 173, 173, 174, 175, 179, 182, 179, 175, 172, 178,
     181, 176, 179, 172, 171, 177, 179, 181, 176, 167, 174]

and the time data is just a constant time apart so something like this

t = np.array([0., 0.04, 0.08, 0.12, 0.16, 0.2, 0.24, 0.28, 0.32, 0.36, 0.4,
              0.44, 0.48, 0.52, 0.56, 0.6, 0.64, 0.68, 0.72, 0.76, 0.8, 0.84,
              0.88, 0.92, 0.96])

The fitted model will be something like this:

y(t) = A * exp(-lambda * t) * cos(omega * t + phi)

Thanks for your help in advance.

Solution

  • This is not an answer but nothing more than a comment. I cannot edit it in the comments section because a picture is absolutely essential and one cannot put a picture in comments.

    If I made no mistake the graphical representation of the data is :

    enter image description here

    This graph doesn't look like a damped sinusodal function. I wonder if one is able to say what kind of function it is. It looks more like an highly scattered linear function.

    Can you roughly sketch (without calculus) the curve that you expect ?