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.

$T + U(x) =$ cosntant $\equiv E$

$\Rightarrow T = E - U(x)$

$\frac{1}{2} m \dot {x}^2 = E -U(x)$

$\dot x = \pm \sqrt{\frac{2\left (E-U(x) \right )}{m}}$

$\int \sqrt{\frac{m}{2\left (E-U(x) \right )}} dx = \int dt$

Forest_UCM_Energy#Energy_for_Linear_1-D_systems