Home/ Questions/Q 7604499
In Process

The Archive Base Latest Questions

Editorial Team
  • 0
Asked: 2026-05-30T23:55:32+00:00

my code for a parametric Lissajous curve: x = A * sin(v * t);

  • 0

my code for a parametric Lissajous curve:

x = A * sin(v * t);
y = B * sin(w * t);


How to calculate the period of this curve above? I have read somewhere that it is the least common multiple (LCM) of v and w but I do not understand what this means. The maximum period of a Lissajous curve is 2 * pi, and I do not understand how LCM(v,w) would yield a value less than 2 * pi. Or is its period pi / LCM(v,w)? Confused…

Share

Leave an answer

You must login to add an answer.

Need An Account,

1 Answer

  1. Editorial Team

    It’s LCM(period(x),period(y))

    = LCM(2*pi/v, 2*pi/w)

    = 2*pi*LCM(1/v, 1/w)

    = 2*pi*LCM(vw/v, vw/w)/vw

    = 2*pi*LCM(w,v)/vw

    = 2*pi/GCF(w,v)

    since LCM(ax,ay) = a*LCM(x,y) and LCM(x,y)*GCF(x,y) = xy.

    Take for example v=2, w=3. The period of x is pi, the period of y is 2*pi/3. The combined period is therefore 2*pi since this is the least common multiple of the two periods. We can calculate this directly as 2*pi*LCM(2,3)/6 = 2*pi, or as 2*pi/GCF(2,3) = 2*pi.

    just as a 2nd example: say w=10, v = 15. Period of x is 2*pi/10, period of y is 2*pi/15, and the least common multiple is 2*pi/5. We can get this directly by 2*pi/GCF(10,15) =2*pi/5 or 2*pi*LCM(10,15)/150 = 2*pi*30/150.

    • 0