A block of mass `m` is connected to another block of mass `M` by a massless spring of spring constant `k`. the blocks are kept of a smooth horizontal plane and are at rest. The spring is unstretched when a constant force `F` starts acting on the block of mass `M` of pull it. Find the maximum extension of the spring

Explanation

We solve the situation in the reference frame of center of mass. As onlyF is the external force acting on the system, due to this force, the acceleration of the center of mass is F/(M + m). Thus with respect to center of mass there is a Pseudo force on the two masses in opposite direction, the free body diagram of m and M with respect to center of mass (taking center of mass at rest) is shown in figure.(mF)/(m+M) Taking centre of mass at rest, if m moves maximum by a distance `x_1` and M moves maximum by a distance `x_2`, then the work done by external forces (including Pseudo force) will be `W=(mF)/(m+M).x_1+(F-(mF)/(m+M)).x_2=(mF)/(m+M).(x_1+x_2)` this work is stored in the form of potential energy of the spring as `U=1/2k(x_1+x_2)^2=(mF)/(m+M).(x_1+x_2)` `x_(mac)=x_1+x_2=(2MF)/(k(m+M))`