In the arrangement given in the figure,if the block of mass $m$ is displaced,the frequency is given by:

$A$ mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude $A$. Its speed as it passes through the equilibrium position is $V$. If extended $2A$ and released,the speed of the mass passing through the equilibrium position will be

$A$ body of mass $4 \ kg$ attached to a spring of force constant $64 \ N \ m^{-1}$ executes simple harmonic motion on a frictionless horizontal surface. The time period of oscillation is

If a spring has time period $T$,and is cut into $n$ equal parts,then the time period of each part will be

$A$ block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 \, cm$ from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The total energy of the block at $x = 5 \, cm$ is $0.25 \, J$. The spring constant of the spring is $......... \, N \, m^{-1}$.

$A$ particle of mass $m$ is attached to three identical massless springs of spring constant $k$ as shown in the figure. The time period of vertical oscillation of the particle is