Two Dimensional Isotropic/Nonisotropic Oscillator

General Initial conditions :    [See info at bottom of page!]

  • X0 =  m     Y0 =  m
  • Initial velocity Vx0  m/s   Vy0 =  m/s
  • wx=  rad/sec   wy =  rad/sec


Information: This is a bare-bones 2D oscillator physlet. You can put in the initial conditions, and the frequencies (thus, basically, the spring constants). Make sure you click UPDATE after changing the numbers.

Isotropic: If the frequencies are equal to each other, then it is ISOTROPIC (both the springs are the same) - you will only be able to get straight lines or ellipses, based on the starting condtions.

Non-Isotropic: Unequal frequencies give a non-isotropic case. Further, if the frequencies are in integer ratio (like 3/5, 2/1, etc.), then you should have a "simple" curve (it won't "fill in" the 2D space), and the frequencies are said to be "commensurate". If there is no integer ratio (an irrational ratio), then the frequencies are incommensurate, and you can have part of the 2D space "fill in" (seemingly randomly).

There is an "animation" in the upper right corner of the screen - depending on your initial conditions, you might go off the screen, but the graph on the lower right is plotting X vs Y, and is set to autoscale, so you'll always be able to see the full motion. The two graphs on the left are to show the X and Y as functions of time (better to compare the frequencies chosen to the motion displayed).