Problem $1(5$pts$)$: The figure below shows a hydraulic cylinder with a pressure source $p_i.$ This pressure drives the piston which moves the load whose mass is $m.$ The piston area is A $,$ and its mass is $m_p.$ The inlet and outlet laminar resistances are $R_1$ and $R_2.$ The outlet exhausts to a pressure $p_d.$ Derive a model of the load displacement $x$ with an input of $p_i($e$.$g$.$ find $($:$x\frac{s}{P_i}(s)$