$A$ 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 .... $s$

$A$ 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.

$P$ and $Q$ are fixed points in the same plane and a mass $m$ is tied by strings as shown in the figure. If the mass is displaced slightly out of this plane and released,it will oscillate with a time period (given $PQ = 2d$,$PR = QR = L$).

$A$ body of mass $0.04 \text{ kg}$ executes simple harmonic motion $(SHM)$ about $x=0$ under the influence of force $F$ as shown in the graph. The time period of the motion is:

$A$ ball is rolling without slipping in a spherical shallow bowl (radius $R$) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled,then the time period of oscillation

$A$ ring is hung on a nail. It can oscillate,without slipping or sliding $(i)$ in its plane with a time period $T_{1}$ and,$(ii)$ back and forth in a direction perpendicular to its plane,with a period $T_{2}$. The ratio $\frac{T_{1}}{T_{2}}$ will be