$A$ 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? 

A block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $\mu$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$. Then,

Initially spring is in natural length and both blocks are in rest condition. Then determine Maximum extension is spring. $k=20 N / M$

When a spring is stretched by $2\,\, cm$ , it stores $100\,\, J$ of energy. If it is stretched further by $2\,\, cm$ , the stored energy will be increased by ............. $\mathrm{J}$

A body of mass $ 0.1 kg $ moving with a velocity of $10 m/s$  hits a spring (fixed at the other end) of force constant $ 1000 N/m $ and comes to rest after compressing the spring. The compression of the spring is .............. $\mathrm{m}$

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
STATEMENT 1 : If stretched by the same amount work
done on $S_1$, Work done on $S_1$ is more than $S_2$
STATEMENT2: $k_1 < k_2$