$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The time for which the moving block remains in contact with the spring will be ... $\sec$.

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation, if their maximum velocities are equal, then the ratio of amplitudes of $A$ and $B$ is

$A$ particle of mass $m$ is attached to four springs with spring constants $k, k, 2k$ and $2k$ as shown in the figure. Four springs are attached to the four corners of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

$A$ block of mass $M_1$ is hung by a light spring of force constant $k$ from the top bar of a reverse $U$-frame of mass $M_2$ resting on the floor. The block is pulled down from its equilibrium position by a distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$-frame will leave the floor momentarily.

$A$ spring is stretched by $0.20\, m$ when a mass of $0.50\, kg$ is suspended. When a mass of $0.25\, kg$ is suspended,its period of oscillation will be .... $sec$ $(g = 10\, m/s^2)$

$A$ spring of force constant $k$ is cut into two parts whose lengths are in the ratio $1:2$. The two parts are now connected as shown and a block of mass $m$ is connected to the combined spring. Find the period of oscillation performed by the block.