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

What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?

A spring whose unstretched length is $\ell $ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where, $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will be

In the adjacent figure, if the incline plane is smooth and the springs are identical, then the period of oscillation of this body is

A spring executes $SHM$ with mass of $10\,kg$ attached to it. The force constant of spring is $10\,N/m$.If at any instant its velocity is $40\,cm/sec$, the displacement will be .... $m$ (where amplitude is $0.5\,m$)

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ is