4-16. For the arrangement shown, x represents the absolute displacement of the mass m, and y is the absolute displacement of the end A of the spring k. Point A is moved according to the relation y = Y sin wrt. (a) Construct the free-body diagram for m. (b) Write the differential equation of motion for m. (c) Obtain bont the solution for the steady-state motion of m. (d) Determine the relation for the impressed force at A. (e) Obtain the expression for the force transmitted to the motion. %3D support at B. y = Y sin wet k wwwA B Problem 4-16

4а. Show that the torque t = la, where I is the rotational inertia. Consider the pulley system shown in figure 4. Suppose the pulley is made up of a disc with mass Ma and a ring (hoop) with mass M, as shown in Figure 4a. Find the moment of inertia I, of the pulley through the center of mass. 4b. Find the angular acceleration a, of the pulley as a function of Ip, 0, M1, M2, µk. You may assume that there is no slipping between the pulley and the rope and the mass of the rope is negligibly small in comparison with the mass M1, and M2. The coefficient of friction between M2 and the incline is µk with M1> M2. 4c. Mr md MK outer ving (Mr) Central dise (Ma) RI axis at RAzti on X- Sedi on a pullag

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 of- mL²; the one to the 27 192 1 mL². Then transform this Fo sin cor right has a mass moment of inertia of- 192 differential equation of the Laplace domain, assuming zero initial conditions. Lastly, compute the damping ratio and damped natural frequency for this system. TET 4 fm o Mo sin or

please define the system and provide the free-body diagram with x-y-axis Please answer these two questions together cause there is a follow-up question.

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