A system consists of two cubes of masses${\text{m}}_{\text{1}}\text{and}{\text{m}}_{\text{2}}$ connected by a spring of spring constant 'k'. Force F is applied on${\text{m}}_{\text{1}}$ along its weight and removed, such that${\text{m}}_{\text{2}}$ is just lifted. Find F  

$x_i$  be the initial compression in the spring

$\text{F}+{\text{m}}_{\text{1}}\text{g}=\text{k}{x}_i$

$x_i=\frac{\text{F}+{\text{m}}_{\text{1}}\text{g}}{\text{k}}$

$x_{\text{f}}$  be the final elongation, when spring lower block lifts 2f

$\text{k}{x}_{\text{f}}={\text{m}}_{\text{2}}\text{g};x_{\text{f}}=\frac{{\text{m}}_{\text{2}}\text{g}}{\text{k}}$

${\text{m}}_{\text{1}}\text{g}\left(x_i+x_{\text{f}}\right)=\frac{1}{2}\text{k}\left(x_i^2-x_{\text{f}}^2\right)$

$\text{F}=\left({\text{m}}_{\text{1}}+{\text{m}}_{\text{2}}\right)\text{g}$