Lissajous Waves

Counterclockwise or clockwise rotation checks out correctly.  Slowing the clock speed lets you check the direction of rotation.  1 - 179 degree of phase angle gives counterclockwise rotation.  181 -359 degrees of phase angle gives clockwise rotation.  0 and 180 degrees of phase angle gives sloped lines. DESMOS Graphing app gives a vertical and horizontal sine wave for these equations and not a Lissajous image.  You have to XY display the two sine waves to get the Lissajous curve displayed. 0 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t - 0) 45 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t -( pi/4)) 90 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t -( pi/2)) 135 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t -(3 pi/4)) 180 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t - pi) 225 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t -( 5pi/4)) 270 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t -( 3pi/2)) 315 phase angle: x(t)=sin(2 X pi x t) y(t)=sin(2 X pi X t -(7pi/4))

published 5 years ago