Derive the equation of motion for the following system, using (the rotation of the beam about the hinge) as the degree-of-freedom. Not that there is an applied force (Fo sin wt) as well as an applied moment (Mo sin wt). The total bar mass is m. Treat the bar as two bars: one to the left of the hinge point; one to the right. The one to the left has a mass moment of inertia ofmL; the one to the 192 Fo sin cor - 4/4 fimo 192 right has a mass moment of inertia of mL. Then transform this differential equation ot the Laplace domain, assuming zero initial conditions. Lastly, compute the damping ratio and damped natural frequency for this system. Mo sin or Derive the equations of motion for the following system using Lagrange's method. Write these equations of motion in matrix form. k m t sinut m, C = x31x m +