Difference between revisions of "Forest UCM Energy Line1D"

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: <math>\dot x = \pm \sqrt{\frac{2\left (E-U(x) \right )}{m}}</math>
 
: <math>\dot x = \pm \sqrt{\frac{2\left (E-U(x) \right )}{m}}</math>
 +
 +
: <math>\int \sqrt{\frac{2\left (E-U(x) \right )}{m}} dx = \int dt </math>
  
  

Revision as of 12:10, 26 September 2014

The equation of motion for a system restricted to 1-D is readily solved from conservation of energy when the force is conservative.

[math]T + U(x) =[/math] cosntant [math]\equiv E[/math]
[math]\Rightarrow T = E - U(x)[/math]
[math] \frac{1}{2} m \dot {x}^2 = E -U(x)[/math]
[math]\dot x = \pm \sqrt{\frac{2\left (E-U(x) \right )}{m}}[/math]
[math]\int \sqrt{\frac{2\left (E-U(x) \right )}{m}} dx = \int dt [/math]




Forest_UCM_Energy#Energy_for_Linear_1-D_systems