$A$ block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

$A$ ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$. The other end of the spring is fixed,and the ring can slide on a smooth horizontal rod as shown. Now,the ring is shifted to position $B$ and released. The speed of the ring when the spring attains its natural length is:

The $P.E.$ of a certain spring when stretched from natural length through a distance $0.3\, m$ is $10\, J$. The amount of work in joule that must be done on this spring to stretch it through an additional distance $0.15\, m$ will be ................ $J$.

$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are,respectively:

If a spring extends by $x$ on loading,then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant).

$A$ spring of spring constant $200 \, Nm^{-1}$ is initially stretched by $10 \, cm$ from the unstretched position. The work to be done to stretch the spring further by another $10 \, cm$ is (in $J$)