In stretching a spring by $2\,cm$ energy stored is given by $U,$ then more stretching by $10\,cm$ energy stored will be

$A$ particle of mass m is constrained to move on $x$ -axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example, when the particle is to the left of $E, F$ points to the right. The magnitude of $F$ is a constant $F$ except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards left from the equilibrium position $E$ and released from rest at $t = 0.$  What is the period of the motion? 

Two particles with mass $m_1$ = $16\ kg$ and $m_2$ = $2\ kg$ slide as 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 diagram. What is the relative velocity of separation in $ms^{-1}$ , after the particles lose contact? …………….$m/s$

 spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring some elongation and released. the block will have maximum velocity when

A block of mass $\sqrt{2}\,kg$ is released from the top of an inclined smooth surface as shown in figure. If spring constant of spring is $100\,N / m$ and block comes to rest after compressing the spring by $1 \,m$, then the distance travelled by block before it comes to rest is ……… $m$