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. The amplitude of oscillations is

$A$ block of mass $1 \; kg$ is fastened to a spring with a spring constant of $50 \; N m^{-1}$. The block is pulled to a distance $x = 10 \; cm$ from its equilibrium position at $x = 0$ on a frictionless surface and released from rest at $t = 0$. Calculate the kinetic,potential,and total energies of the block when it is $5 \; cm$ away from the mean position.

$A$ bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$. The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of time period $T$. If the mass is increased by $m$,the time period becomes $5T/3$. Then the ratio of $m/M$ is

$A$ clock is designed based on the oscillations of a spring-block system suspended vertically in the absence of air resistance. Assume it shows the correct time when a spring of stiffness $k$ and a block of mass $m$ are used. If the block is replaced by another block of mass $4m$,choose the correct option.

$A$ $10 \,kg$ metal block is attached to a spring of spring constant $1000 \,N \,m^{-1}$. The block is displaced from the equilibrium position by $10 \,cm$ and released. The maximum acceleration of the block is: (in $\,m/s^2$)