The height of a liquid column in a $U$-tube is $0.3 \ m$. If the liquid in one of the limbs is depressed and then released,the time period of the liquid column will be $....... \ s$.

$9 \text{ kg}$ of solution is poured into a glass $U$-tube as shown in the figure. The tube's inner diameter is $2 \sqrt{\frac{\pi}{5}} \text{ m}$ and the solution oscillates freely up and down about its position of equilibrium $(x=0)$. The period of oscillation in seconds is (Given: $1 \text{ m}^3$ of solution has a mass $\rho=900 \text{ kg/m}^3$,$g=10 \text{ m/s}^2$,ignore frictional and surface tension effects).

In both figures shown below, there is a hole along the diameter of the Earth. In the first figure, a particle is released from point $A$ and it oscillates with a time period $T_1$. In the second figure, the same particle is released from point $B$ and it oscillates with a time period $T_2$. Then, [$O$ is the centre of the Earth]

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

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.)

$A$ 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,and it starts oscillating with frequency $n$. The frequency $n$ is equal to (where $g$ is the acceleration due to gravity):