$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ ($x$ and $y$ in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

$A$ light hollow cube of side length $10 \ cm$ and mass $10 \ g$ is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \ s$,where the value of $y$ is (Acceleration due to gravity,$g = 10 \ m/s^2$,density of water $\rho = 10^3 \ kg/m^3$)

$A$ cylindrical block of mass $M$ and area of cross-section $A$ is floating in a liquid of density $\rho$ with its axis vertical. When depressed a little and released, the block starts oscillating. The period of oscillation is . . . . . . . . . . .

If a body is released into a tunnel dug across the diameter of the Earth,it executes simple harmonic motion with a time period of:

$A$ bead of mass $m$ is attached to the mid-point of a taut,weightless string of length $l$ and placed on a frictionless horizontal table. Under a small transverse displacement $x$,as shown in the figure,if the tension in the string is $T$,then the frequency of oscillation is:

$A$ rectangular block of mass '$m$' and cross-sectional area '$A$' floats on a liquid of density '$\rho$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency ($g$ = acceleration due to gravity).