$A$ test tube of mass $6 \ g$ and uniform area of cross-section $10 \ cm^2$ is floating in water vertically when $10 \ g$ of mercury is in the bottom. The tube is depressed by a small amount and then released. The time period of oscillation is (Acceleration due to gravity $= 10 \ m/s^2$) (in $s$)

$A$ 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 ....... $s$.

The potential energy of a particle of mass $1\,kg$ in motion along the $x-$axis is given by $U = 4(1 - \cos 2x)\,J,$ where $x$ is in $meters$. The period of small oscillations (in $sec$) 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

If the maximum velocity and maximum acceleration of a particle executing $SHM$ are equal in magnitude,the time period will be .... $\sec$

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$, it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, what will be its new time period in seconds?