$($a$)$ The system in Figure $1$a represents the landing strut of an aircraft. Chamber $1$ on the right is fixed, and as the piston rod moves inward $($to the right$),$ it compresses the oil located inside. The compliance of the fluid in Chamber $1$ is C$1$C$1.$ Chamber $3$ on the left is connected to two compliances, C$2$C$2$ and C$3$C$3,$ corresponding to the pistons, and acts as a reservoir for the landing gear. The piston has a hole $($orifice$)$ through which the rod passes, with an enlarged cross$-$sectional area at the tip.

Thus, as the piston moves inward $($to the right$),$ the orifice area changes. This orifice is modeled as a fluid resistance RR$.$ As the piston moves to the right, the oil flows through Chamber $2$ into Chamber $3$ via the orifice. Consequently, Chamber $2$ experiences a higher pressure than Chamber $3,$ and this pressure difference increases as the piston moves to the right $($the resistance RR is higher when the orifice area decreases$).$ This pressure difference is counterbalanced by the applied force FF exerted by the hydraulic fluid on the piston as it moves to the left.

This behavior allows the piston to absorb the vertical force acting on the landing strut during the aircraft's descent.

$($i$)$ Draw the bond graph and assign causality to all the bonds.

$($ii$)$ Assign causality to the junctions. State whether there is any conflict