The plucked string.

(Edit:  the wxMaxima calculus books are done)

 

Today I used a Fourier expansion to animate the behavior of a plucked string subject to frequency-dependent damping.  The pluck is modeled by a sharp triangular pulse in the initial state.  This is a good way to visualize what happens on a guitar string:  the motion of the string is the superposition of many standing waves of different frequencies, but the higher frequencies die out faster than the lower ones.  Eventually all that remains is the fundamental mode (the lowest note sounded by the string).  I plan to write up a proper article in the next month to address the mathematics and the CAS coding behind the animation.  Enjoy the movie!

maxout_12

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