A disk of radius $$R$$ with uniform positive charge density $$\sigma$$ is placed on the $$xy$$ plane with its center at the origin. The Coulomb potential along the z-axis is

$$V(z) = \dfrac{\sigma}{2\epsilon_0}\left(\sqrt{R^2 + z^2} - z\right)$$

A particle of positive charge $$q$$ is placed initially at rest at a point on the z axis with $$z = z_0$$ and $$z_0 > 0$$. In addition to the Coulomb force, the particle experiences a vertical force $$\vec{F} = -c\hat{k}$$ with $$c > 0$$. Let $$\beta = \dfrac{2c\epsilon_0}{q\sigma}$$. Which of the following statement(s) is(are) correct?