The frequency of oscillation of a mass $m$ suspended by a spring is $v$. If the mass is reduced to one-fourth,what will be the new frequency of oscillation?

$A$ solid cylinder of density $\rho_0$,cross-section area $A$ and length $l$ floats in a liquid of density $\rho (\rho > \rho_0)$ with its axis vertical. If it is slightly displaced downward and released,the time period of oscillation will be:

$A$ mass on a vertical spring begins its motion at rest at $y = 0 \ cm$. It reaches a maximum height of $y = 10 \ cm$. The two forces acting on the mass are gravity and the spring force. The graph of its kinetic energy $(KE)$ versus position is given below. Net force on the mass varies with $y$ as

$A$ particle of mass $1 \, \text{kg}$ is hanging from a spring of force constant $100 \, \text{N/m}$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period $T$. The time when the kinetic energy and potential energy of the system will become equal is $\frac{T}{x}$. The value of $x$ is ..... .

Three masses $700 \,g$, $500 \,g$, and $400 \,g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $700 \,g$ mass is removed, the system oscillates with a time period of $3 \,s$. If the $500 \,g$ mass is further removed, then it will oscillate with a period of

$A$ stiff spring having spring constant $k = 400 \text{ N/m}$ is attached to the floor vertically. $A$ mass $m = 10 \text{ kg}$ is placed on top of the spring. The block oscillates if it is pressed downward and released. Find the extension in the spring at which the block loses contact with the spring. (Take $g = 10 \text{ m/s}^2$) (in $\text{ cm}$)