In the reported figure, two bodies $A$ and $B$ of masses $200\, {g}$ and $800\, {g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $.....\,{rad} / {s}$ when ${k}=20 \,{N} / {m} .$

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

A man weighing $60\  kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\  m$ and frequency $\frac{2}{\pi } Hz$. Which of the following staements is correct

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be

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

A spring with $10$ coils has spring constant $k$. It is exactly cut into two halves, then each of these new springs will have a spring constant