I have been reviewing this article on piano hammer dynamics:
https://www.acs.psu.edu/drussell/Publications/pianohammer.pdf
They describe the impact of a piano hammer to have ideally perhaps a sine-squared impulse shape, which can be graphed as follows:
https://www.desmos.com/calculator/br9dxcfeb3
However, they state in practice:
"The asymmetry in the measured pulse is due to the hysteresis of the hammer felt. The measured pulse is compared with a half-sine pulse, a sine-squared pulse, and a skewed versed-sine pulse (the product of a decaying exponential and a sine-squared pulse) in Figure 3 (a), (b), and(c), respectively. These three shapes were chosen not only because they fit the data rather well, but also because they are shock shapes whose shock spectra are well documented in the literature"
Graphics here:
How would I go about graphing such a skewed sine wave that peaks at y=1 as they do here?
I do not understand the math they are implying when they say "a skewed versed-sine pulse (the product of a decaying exponential and a sine-squared pulse)".
Can anyone spell it out for me? Thanks.
Edit: Is it as simple as this? I think I got it: https://www.desmos.com/calculator/v0yj7i76qf