Finding the perfect damp for a sinusoid graph

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Below is a sinusoid function that is defined by this equation: $ 9.36 \times\sin(0.95x-2.06)+13.64 $. Would it be possible to create a function that produces a dampening close to the following: enter image description here

If this is not possible, can a fitting like this can be done? enter image description here

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They are not enough points and too large scatter for a good fitting.

Example of poor fit below of sinusoidal function damped with exponential.

enter image description here