Forest UCM Energy Line1D

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{m}{2\left (E-U(x) \right )} dx = \int dt [/math]

Forest_UCM_Energy#Energy_for_Linear_1-D_systems