A particle of mass m is located in a one dimensional potential field $$U(x) = U_0(1 - \cos ax)$$ where $$U_0$$ and $$a$$ are constants. Which of the following statement or statements is or are correct?

A

The particle will execute Simple Harmonic Motion for small displacements

B

The stable equilibrium condition is $$x = 0$$

C

The time period of small oscillations is $$\frac{2\pi}{a}\sqrt{\frac{m}{U_0}}$$

D

The angular frequency for small oscillations is $$a\sqrt{\frac{U_0}{m}}$$