$A$ block of mass $m$ attached to one end of a vertical spring produces an extension $x$. If the block is pulled and released,the periodic time of oscillation is:

$A$ block of mass $1 \; kg$ is fastened to a spring with a spring constant of $50 \; N m^{-1}$. The block is pulled to a distance $x = 10 \; cm$ from its equilibrium position at $x = 0$ on a frictionless surface and released from rest at $t = 0$. Calculate the kinetic,potential,and total energies of the block when it is $5 \; cm$ away from the mean position.

$A$ particle is suspended from a vertical spring which is executing $S.H.M.$ of frequency $5 \ Hz$. The spring is unstretched at the highest point of oscillation. What is the maximum speed of the particle? (Take $g = 10 \ m/s^2$)

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of period $T$. If the mass is increased by $m$,the time period becomes $\frac{5T}{3}$. What is the ratio $\left(\frac{M}{m}\right)$?

Three masses $700 \,g$, $500 \,g$, and $400 \,g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $700 \,g$ mass is removed, the system oscillates with a time period of $3 \,s$. If the $500 \,g$ mass is further removed, then it will oscillate with a period of

Two massless springs with spring constants $2k$ and $9k$ carry $50\,g$ and $100\,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then,the ratio of their respective amplitudes will be