Fill in the blank: The force constant of a spring is $0.5 \, Nm^{-1}$. The force necessary to increase the length of the spring by $10 \, cm$ will be .......... (in $, N$)

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

Initially,the spring is at its natural length and both blocks are at rest. Determine the maximum extension in the spring. Given $k = 20 \ N/m$,$m_1 = 0.5 \ kg$,$m_2 = 1 \ kg$,and $F = 1 \ N$.

An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

Two blocks are connected by a spring. The combination is suspended,at rest,from a string attached to the ceiling,as shown in the figure. The string breaks suddenly. Immediately after the string breaks,what is the initial downward acceleration of the upper block of mass $2m$?

Two massless springs of spring constants $K_1$ and $K_2$ are connected in series, suspended vertically, and a mass is attached to the free end. If $x_1$ and $x_2$ are their respective extensions and $F$ is the stretching force, what is the total extension produced?