Answer to Question #207353 in Classical Mechanics for Aysu

Question

Find the law of motion of a particle in the field U(x) = – Bx², if its total energy is zero (B is positive constant). 

Answer 1

$$F=\frac{dU}{dx}=-2Bx\\ma=-2Bx\\\omega=\sqrt{\frac{2B}{m}}\\x=A\cos{(\omega t+\phi)}$$