$A$ body of mass $0.01\, kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown in the graph. The period of the $S.H.M.$ is .... $s$

$A$ drinking straw is dipped in a pan of water to a depth $d$ from the surface (see figure). Water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result,its height $y$ from the surface of the water varies periodically. Ignoring damping,the equation for $y$ is ($g$ is the acceleration due to gravity):

The potential energy of a particle of mass $10 \ g$ as a function of displacement $x$ is $(50 x^2 + 100) \ J$. The frequency of oscillation is

$A$ 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.

$A$ 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:

$A$ rectangular block of mass $m$ and cross-sectional area $A$ floats in a liquid of density $\rho$. If we give it a small vertical displacement from equilibrium,it undergoes $SHM$ with a time period $T$. Then: