Difference between revisions of "Forest UCM Energy Line1D"

Revision as of 12:11, 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.

$T + U(x) =$ cosntant

$\equiv E$

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

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

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

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

Revision as of 12:11, 26 September 2014 (view source) Foretony (talk \| contribs) ← Older edit		Revision as of 12:11, 26 September 2014 (view source) Foretony (talk \| contribs) Newer edit →
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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{m}2\left (E-U(x) \right )}{} dx = \int dt </math>	+	: <math>\int \sqrt{\frac{m}{2\left (E-U(x) \right )} dx = \int dt </math>