2 problems here: What is the force pulling $m_2$ when $m_1$ falls? I can only think of tension. When $m_1$ does fall (maybe a height $H$), does $m_2$ move $H/2$ to the right? Since the other end of the rope is attached to the support of the pulley, and thus can't move.
Also, the coefficient of static/dynamic friction between $m_1$ and the table is $\mu_s$ and $\mu_k$
Usually these beginner Atwood Machine problems were easy, since the ones I did were two masses attached to a taut rope, (then their displacement would be equal) but this is something entirely different.