$A$ block of mass $M = 5 \ kg$ is suspended from one end of a spring. The spring extends by $l = 0.1 \ m$ due to the mass of the block. The block is given an upward velocity of $v = 2 \ m/s$. What is the maximum height $h$ (in $m$) reached by the block? $(g = 10 \ m/s^2)$

When a body of mass $8 \,kg$ is attached to a spring balance, the reading of the balance is $20 \,cm$. Instead of $8 \,kg$, if another body of mass $M$ is suspended from the spring balance and is made to oscillate vertically, the time period of oscillation is $\frac{\pi}{5} \,s$, then the value of $M$ is (Acceleration due to gravity $= 10 \,m/s^2$) (in $\,kg$)

$A$ spring-block system in horizontal oscillation has a time period $T$. If the spring is cut into four equal parts and the block is re-connected with one of the parts,what will be the new time period of oscillation?

$A$ sphere of mass $m$ is attached to the lower end of a light vertical spring with force constant $k$. The upper end of the spring is fixed. The sphere is released from rest at the natural (unstretched) length of the spring and comes to rest again after falling through a distance $x$.

$A$ block of mass $5 \ kg$ moves along the $x$-direction subject to the force $F = (-20x + 10) \ N$,with the value of $x$ in metre. At time $t = 0 \ s$,it is at rest at position $x = 1 \ m$. The position and momentum of the block at $t = (\pi / 4) \ s$ are

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