springs are in series!

A single string went through all the pulleys, so all springs had the same tension in them, that is, k1x1=k2x2=k3x3=k4x4=2T

and recall, when springs are in series, the same force acts through them!

So, the whole problem reduces to this

or if one wants to spend a lil more time but wants to go through basics, he should form these equations

1)T=ma...(neglecting mg for calculation of time period)

2)equilibria of massless pulleys; k1x1=k2x2=k3x3=k4x4=2T, k1=k2=k3=k4, means x1=x2=x3=x4

3)length constraint, 2(x1+x2+x3+x4)+x=0, where x is displacement of block

Using these equations, find a relation of the form Kx=-ma, determine K, and all is done

yes, X=4