The vertical extension in a light spring by a weight of $1\, kg$ suspended from it is $9.8\, cm$. What is the period of oscillation?

$A$ heavy brass sphere is hung from a light spring and is set in vertical small oscillations with a period $T$. The sphere is now immersed in a non-viscous liquid with a density $1/10$th the density of the sphere. If the system is now set in vertical $S.H.M.$,its period will be

$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

Two springs,of force constants $k_1$ and $k_2$,are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values,the frequency of oscillation becomes

In the figure given below,a block of mass $M = 490 \, g$ placed on a frictionless table is connected with two springs having the same spring constant $(K = 2 \, N \, m^{-1})$. If the block is horizontally displaced through '$X$' m,then the number of complete oscillations it will make in $14 \pi$ seconds will be $.........$

The potential energy of a particle of mass $4 \, kg$ in motion along the $x$-axis is given by $U = 4(1 - \cos 4x) \, J$. The time period of the particle for small oscillations $(\sin \theta \simeq \theta)$ is $\left(\frac{\pi}{K}\right) \, s$. The value of $K$ is .......