A block $P$ of mass $m$ is placed on a smooth horizontal surface. A block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is ${\mu _S}$. A spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is

Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$

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 $0.5\,m$)

The spring mass system oscillating horizontally. What will be the effect on the time period if the spring is made to oscillate vertically ?

The time period of simple harmonic motion of mass $\mathrm{M}$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$, where the value of $\alpha$ is____.

When a mass $m$ is hung from the lower end of a spring of neglibgible mass, an extension $x$ is produced in the spring. The time period of oscillation is