6a. 6b. Draw free body diagrams and write equations of motion for x and 0 of the cylindrical mass in the following system. Use a right-hand coordinate system where > 0 for counterclockwise rotation. Assume pure rotation for the cylinder (no slip), but take into account the cylinder's mass and rotational inertia (use Jcylinder = mR). 1 Here F(t) is an applied force. Hint 1: Static friction is a contact force, so carefully consider where to place it. Hint 2: There are not many torques acting on the cylinder. x(t) Cylinder, mass m wwwww. k R "(+) C Pure rolling Combine the two equations from part (a) into a single governing equation for x. First reduce to one equation by solving for and eliminating the friction force. Then eliminate 8 using x = -RO. Simplify the resulting equation, moving all x terms to the left-hand side. Note: When using the arc length equation x = +RO we always need to choose a radius and positive/negative sign that agrees with the particular system under consideration.