- #1

humanist rho

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## Homework Statement

A particle of mass m moves in 1D such that it has Lagrangian,

[itex]L=\frac{m^{2}\dot{x}^{4}}{12}+m\dot{x}^{2}V(x)-V_{2}(x)[/itex]

where V is some differentiable function of x.Find equation of motion and describe the nature of motion based on the equation.

## The Attempt at a Solution

Equation of motion is,

[itex]\frac{d}{dt}(\frac{m^{2}\dot{x}^{3}}{3}+2m\dot{x}V(x))-m\dot{x}^{2}\frac{%

\partial V}{\partial x}+\frac{\partial V_{2}}{\partial x}=0[/itex]

[itex]m^{2}\dot{x}^{2}\ddot{x}+2m\ddot{x}V(x)-m\dot{x}^{2}\frac{\partial V}{%

\partial x}+\frac{\partial V_{2}}{\partial x}=0[/itex]

How can i predict nature of motion from this?

Thanks.