When the acceleration of the $5\ kg$ block is $2\ m/s^2$ as shown in the figure,what will be the acceleration of the $15\ kg$ block? (in $m/s^2$)

Two masses of $1 \, kg$ and $2 \, kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $20 \, N$ acts on the $2 \, kg$ mass. At the instant when the $1 \, kg$ mass has an acceleration of $10 \, m/s^2$ towards the right,the acceleration of the $2 \, kg$ mass is ......... $m/s^2$.

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 $F = 1 \ N$.

Two springs,$P$ and $Q$,of force constants $k_P$ and $k_Q$ (where $k_Q = k_P / 2$) are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$,then the energy stored in $P$ 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 $2m$?

$A$ spring has length $L$ and force constant $K$. It is cut into two springs of length $L_1$ and $L_2$ such that $L_1 = N L_2$ ($N$ is an integer). The force constant of the spring of length $L_1$ is: