$3)$ A small hydraulic jack is shown below. At this instant, a $10-$lb force is applied to the handle. This causes the $3\mathrm{.}5$ in link to rotate clockwise at a constant rate of $\backslash (5\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The weight of link $2$ and $3$ are $0\mathrm{.}5$ lb and $1$ lb respectively. Link $4$ is $1\mathrm{.}5$ lb $.$ Determine the following: $($use $\backslash (\backslash$mathrm$\{$I$\}\_\{\backslash$mathrm$\{$G$\}\}=\backslash$mathrm$\{$ML$\}^\{2\}/12\backslash ))$

a$)$ The linear acceleration of the piston

b$)$ The inertial force of link $4$

c$)$ the pin forces

d$)$ The force developed on the piston due to the hydraulic fluid

e$)$ Solve part d$)$ by using the Energy Equations $($Power Balance$)$