Difference between revisions of "Forest UCM Osc 2-DOsc"

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The equations of motion are separable two equations, one for each direction
 
The equations of motion are separable two equations, one for each direction
  
: <math>\ddot x = - \omega^2x</math>
+
: <math>\ddot x = - \omega^2x \Rightarrow x = A_x \cos(\omega t - \delta_x)</math>
: <math>\ddot y = - \omega^2 y</math>
+
: <math>\ddot y = - \omega^2 y \Rightarrow y = A_y \cos(\omega t - \delta_y)</math>
  
  
 
[[Forest_UCM_Osc#2-D_Oscillators]]
 
[[Forest_UCM_Osc#2-D_Oscillators]]

Revision as of 14:46, 4 October 2014

Two Dimensional Oscillators

Isotropic Oscillator

The simplest 2-D oscillator that is composed of identical springs (same spring constant).

[math] \vec F = -k( x \hat i + y \hat j)[/math]

The equations of motion are separable two equations, one for each direction

[math]\ddot x = - \omega^2x \Rightarrow x = A_x \cos(\omega t - \delta_x)[/math]
[math]\ddot y = - \omega^2 y \Rightarrow y = A_y \cos(\omega t - \delta_y)[/math]


Forest_UCM_Osc#2-D_Oscillators