2 blocks of 'm' are connected to a spring at rest at opposite ends. A pulling force of F on one of the blocks is away from the other one.

Extension of string= Xo

(A)

Suppose the displacement of the first block is x₁ ànd that of second is x₂, then

X=(mx1+mx2)/2m or Ft²/4m=(x1+x2)/2

So x1+x2=Ft²/2m......(1)

And, the extension of the spring is x1-x2=x0........(2)

From 1 and 2

X1=1/2[(Ft²/2m)+x0] and - for x2

(B)The acceleration of the centre of mass is 

a_com=F/2m

The displacement of the centre of the mass at time t will be

X=1/2a_comt²=Ft²/4m

(A)

Suppose the displacement of the first block is x₁ ànd that of second is x₂, then

X=(mx1+mx2)/2m or Ft²/4m=(x1+x2)/2

So x1+x2=Ft²/2m......(1)

And, the extension of the spring is x1-x2=x0........(2)

From 1 and 2

X1=1/2[(Ft²/2m)+x0] and - for x2