$9 \ kg$ of mercury is poured into a glass $U$-tube with an inner diameter of $1.2 \ cm$. The mercury can flow without friction within the tube. The oscillation period is ......... $\sec$. (Density of mercury $\rho = 13.6 \times 10^3 \ kg/m^3$)

$A$ 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 $\rho = 10^3 \ kg/m^3$)

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.)

The ends of a rod of length $l$ and mass $m$ are attached to two identical springs. The rod is free to rotate about its centre $O$. The rod is depressed slightly at end $A$ and released. The time period of the resulting oscillation is

$A$ particle executes linear $S.H.M.$ with amplitude $4 \ cm$. The magnitude of velocity and acceleration is equal when it is at $3 \ cm$ from the mean position. The time period of oscillation is:

$A$ ring whose diameter is $1 \ m$ oscillates simple harmonically in a vertical plane about a nail fixed at its circumference. The time period will be ....... $s$.