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How would I fit a curve to the maximum values of a data set, to fit a curve for logarithmic decrement?

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I'm looking to fit a curve from a measured data set in order to calculate the logarithmic decrement, and eventually a damping ratio. The issue I'm running into is how to fit an exponential curve to the maximum values of the data? I've taken it and only looking at half of the signal (say positive only) but still no luck in getting it figured out. See plots below showing what I'm looking to do.

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