Answer to Question #209220 in Classical Mechanics for İlkin

Question

8. Find the law of motion of a particle in the field U(x)=-Cx^4 ,if it is Total energy is zero ( C is positive constant)

Answer 1

$F=U'=-4cx^3,$

$F=\frac Ux=-cx^3,$

$F=-5cx^3,$

$F=m\ddot x,$

$\ddot x=\frac Fm=-\frac{5cx^3}{m},$

$\dot x=-\frac{5cx^4}{4m},$

$x=-\frac{cx^5}{4m},$

$(-\frac{cx^5}{4m})^2-\omega^2\frac{5cx^3}{m}=0,$

$cx^7-80\omega^2 m=0.$