$A$ block of mass $m$ is released suddenly from the top of a spring with a spring constant $k$. $(i)$ What will be the maximum compression in the spring? $(ii)$ What will be the compression in the spring at the equilibrium position?

$A$ spring of force constant $k$ is cut into three equal parts. The force constant of each part would be

One-fourth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will be

Two springs $A$ and $B$ having spring constants $K_{A}$ and $K_{B}$ $(K_{A} = 2 K_{B})$ are stretched by applying forces of equal magnitude. If the energy stored in spring $A$ is $E_{A}$,then the energy stored in spring $B$ will be:

Two blocks with masses $100 \text{ g}$ and $200 \text{ g}$ are attached to the ends of springs $A$ and $B$ as shown in the figure. The energy stored in spring $A$ is $E$. The energy stored in spring $B$, when the spring constants $k_{A}$ and $k_{B}$ of springs $A$ and $B$ respectively satisfy the relation $4k_{A} = 3k_{B}$, is:

Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is