$2.(20$ points$)$ Analyze the acceleration of the links in the following slider$-$crank. The input is the rotation of the crank $($link $2).$ The angular velocity of the link $2$ is denoted as $\backslash (\backslash$omega$\_\{2\}\backslash )$ and the angular acceleration is $\backslash (\backslash$alpha$\_\{2\}\backslash ).$ Use the method of kinematic coefficients to write down necessary equations to obtain the angular velocity and acceleration of the link $3,$ and the velocity of and acceleration of the slider $($link $4).$ You need to start from necessary vector loop then perform position, velocity, and acceleration analyses. Write down the unknowns to be solved from each set of equations.