Forest UCM Energy Line1D

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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]




Forest_UCM_Energy#Energy_for_Linear_1-D_systems