= Plucked string model
Staring from a <#triangle wave>, this explains why we always get the same musical notes:
* https://www.math.hmc.edu/~ajb/PCMI/lecture7.pdf "7.5.1. Musical instruments" is very good. Also mentions that in the <piano> it is more like an initial speed is applied, and it is not the same as plucking
* https://music.stackexchange.com/questions/135635/confusion-about-overtones-and-a-slow-motion-video-of-a-plucked-string
* https://music.stackexchange.com/questions/60833/what-determines-the-relative-volumes-of-the-harmonics-when-plucking-a-guitar-str
See also: <solving partial differential equations with the Fourier series>.
TODO: do higher overtones decay faster in time than the base ones?
* https://www.physicsforums.com/threads/why-do-harmonics-decay-faster-than-the-fundamental.955731/ But presumaby yes, damping force is proportional to speed, and higher harmonics have higher speeds going up and down
\Video[https://www.youtube.com/watch?v=_X72on6CSL0]
{title=Motion of Plucked String by Dan Russell}
\Video[https://www.youtube.com/watch?v=Qr_rxqwc1jE]
{title=Slow motion: rubber string pulled and released by Pavel Radzivilovsky}
{description=
Good symmetric example. But unfortunately the video is too short.
Featured at: https://www.reddit.com/r/Physics/comments/kyocxr/what_happens_when_a_plucked_string_is_released/
}
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