$A$ ball of mass $m$ is dropped from a height $h$ on a platform fixed at the top of a vertical spring,as shown in the figure. The platform is depressed by a distance $x$. Then the spring constant is

$A$ 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.

Two particles with mass $m_1 = 16 \ kg$ and $m_2 = 2 \ kg$ slide as a unit with a common velocity of $12 \ ms^{-1}$ on a level frictionless surface. Between them is a compressed massless spring with spring constant $k = 100 \ Nm^{-1}$. The spring,originally compressed by $25 \ cm$,is suddenly released,sending the two masses,which are connected to the spring,flying apart from each other. The orientation of the spring w.r.t. the initial velocity is shown in the diagram. What is the relative velocity of separation in $ms^{-1}$,after the particles lose contact?

If a spring extends by $x$ on loading,then the energy stored in the spring is (where $T$ is the tension in the spring and $K$ is the spring constant):

In the figure,the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage,the minimum mass of $A$ must be

$A$ block of mass $100 \ g$ moving at a speed of $2 \ m \ s^{-1}$ compresses a spring through a distance $2 \ cm$ before its speed is halved. Find the spring constant of the spring. (in $N \ m^{-1}$)