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 on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched when a constant force F starts acting on the block of mass M to pull it. Find the max. extension of the spring.
The Attempt at a Solution
I can find the answer working from the reference frame of COM of the system of 2 blocks and spring.
I am interested in finding it from ground frame.
Net force on M, F1 = F-kx, where x is the extension in the spring
Net force on m, F2 = kx
Let the displacements of the two blocks be x1 and x2.
F1x1 + F2x2 =0.5k(x2-x1)2 (x2-x1 is the extension produced)
I am unable to find another equation.