Swallow Curve
A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity.
A typical harmonograph has two pendulums that move in such a fashion, and a pen that is moved by two perpendicular rods connected to these pendulums. Therefore, the path of the harmonograph figure is described by the parametric equations
&space;=&space;A_1&space;\sin&space;(f_1&space;t&space;+&space;p_1)&space;e^{-d_1t}&space;+&space;A_2&space;\sin(f_2&space;t&space;+&space;p_2)&space;e^{-d_2&space;t}&space;\\&space;y(t)&space;=&space;A_3&space;\sin&space;(f_3&space;t&space;+&space;p_3)&space;e^{-d_3t}&space;+&space;A_4&space;\sin(f_4&space;t&space;+&space;p_4)&space;e^{-d_4&space;t}&space;\end{align*})
The swallow curve has parameters
&space;\\&space;&f&space;=&space;(2,&space;1,&space;9,&space;6)&space;\\&space;&p&space;=&space;(0,&space;\pi,&space;\pi/2,&space;\pi/2)&space;\\&space;&d&space;=&space;(0.02,&space;0.002,&space;0.02,&space;0.002)\\&space;\end{align*})
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