Turning a simple mech. problem into an olympiad one

[wrobel]

There is a nice sheet of mechanics problems: Kalda
I once shared this link on the PF.
Consider problem pr33. Since this problem is very simple let us modify it a bit. Namely assume that the left block has the same initial velocity:

The question is the same. I suspect that now it is an olympiad problem indeed. :)
My guess is to write down the Lagrange equations for the system with three degrees of freedom and expand the corresponding solution using the Taylor formula up to at least $O(t^4)$ .

 

[anuttarasammyak]

My guess. Long thread and small v make net torque by gravity negligible and almost conserve blocks angular momentum of counter clock wise direction
which turns the pulley and pulls up the right block.