Two blocks of masses m₁ and m₂ being connected with a light spring of stiffness k are driven with forces F₁ and F₂ on a smooth horizontal plane. If the blocks move with same acceleration a₀,  the value of a₀ is:

In the given system, the spring force due to spring on the masses is internal force. The acceleration of system is due to external forces only. Here we can assume the two blocks as one system and their acceleration is given as

$a_0=\frac{\text{ Net force towards motion of masses }}{\text{ Total mass }}$

$a_0=\frac{{\mathrm{F}}_1-{\mathrm{F}}_2}{{ \mathrm{m}}_1+{\mathrm{m}}_2}$

${\mathrm{a}}_0=\frac{{\mathrm{F}}_1-{\mathrm{F}}_2}{{ \mathrm{m}}_1+{\mathrm{m}}_2}$