(Solved): (a) For the dynamic system shown in the figure below derive the governing equation in terms of the ...

(a) For the dynamic system shown in the figure below derive the governing equation in terms of the displacement $y$ of the block $m_2$. Pulleys are assumed massless; friction between the block $m_2$ and the surface of the incline is negligible $\left({?}_d=0\right)$. Determine the smallest value of $m_1$ that can lift $m_2$. (b) Assume that the system can be started to overcome static friction, which is no longer negligible. If $m_1=\frac{1}{2}{m}_2$, how large can ${?}_d$ become before $m_l$ can no longer lift $m_2$.