A block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact is

A mass $m = 1.0\,kg$ is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is $500\,N/m.$ What is the amplitude $A$ of the motion, so that the mass $m$ tends to get detached from the pan ? (Take $g = 10\,m/s^2$ ). The spring is stiff enough so that it does not get distorted during the motion.

Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction is

One-forth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will be

Two masses $m_1$ and $m_2$ are supended 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 vibration is

The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be