What factors determine the natural frequency of oscillation of a body?

$A$ sphere of radius $r$ is kept on a concave mirror of radius of curvature $R$. The arrangement is kept on a horizontal table (the surface of the concave mirror is frictionless and the sphere is sliding,not rolling). If the sphere is displaced from its equilibrium position and released,it executes $S.H.M.$ The period of oscillation will be

$A$ number of holes are drilled along a diameter of a disc of radius $R$. To get the minimum time period of oscillations,the disc should be suspended from a horizontal axis passing through a hole whose distance from the centre should be:

Under the influence of force $F_1$,a body oscillates with a period $T_1$,and due to another force $F_2$,the body oscillates with a period $T_2$. If both forces act simultaneously,what is the resultant period? (Consider the displacement is the same in all three cases.)

$A$ cylindrical log of wood of height $h$ and area of cross-section $A$ floats in water. It is pressed and then released. Show that the log would execute $SHM$ with a time period $T = 2\pi \sqrt{\frac{m}{A\rho g}}$,where $m$ is the mass of the body and $\rho$ is the density of the liquid.

$A$ particle of mass $m$ is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k|x|^3$,where $k$ is a positive constant. If the amplitude of oscillation is $a$,then its time period $T$ is: