Consider the following $2$ mass and pulley system where $m_1=13kg,{}_s=0\mathrm{.}4,$ and ${}_k=0\mathrm{.}3$

a$.$ What is the maximum value of $m_2$ at which $m_1$ will remain motionless?

b$.$ Using that value $m_2$ found in part a$),$ how far will $m_2$ fall in $2$ sec if $m_1$ somehow acquires an initial

velocity of $0\mathrm{.}2\frac{m}{s}$ to the right?