$(15)$ Multi$-$mass system. Assume that all masses slide with negligible friction, and that the pulley wheel

s negligible mass.

a$.$ How many degrees of freedom does this system have? Explain your reasoning.

b$.$ Identify any inputs to this system $($i$.$e$.$ what forces and$/$or displacements don't depend on

position, velocity, or acceleration of a mass$).$

c$.$ Write a kinematic constraint for this system.

d$.$ Draw a free body diagram for each mass. Indicate direction of positive acceleration in each.

e$.$ Find Equations of Motion for this system, and report in matrix form.