$A$ spring having a spring constant $K$ is loaded with a mass $m$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is

$A$ mass of $200 \text{ g}$ is suspended from a spring with a force constant of $80 \text{ N/m}$. What is the time period of the oscillation in seconds?

Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $k$. When the masses are in equilibrium,$m_1$ is removed without disturbing the system. Then the angular frequency of oscillation of $m_2$ is

When a body of mass $1.0 \,kg$ is suspended from a certain light spring hanging vertically, its length increases by $5 \,cm$. By suspending a $2.0 \,kg$ block to the spring and if the block is pulled through $10 \,cm$ and released, the maximum velocity in $m/s$ is: (Acceleration due to gravity $= 10 \,m/s^2$)

$A$ block $P$ of mass $m$ is placed on a smooth horizontal surface. $A$ block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is $\mu_S$. $A$ spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the blocks is

The angular frequency of a block of mass $0.1 \ kg$ oscillating with the help of a spring of force constant $2.5 \ Nm^{-1}$ is