5- A pulley 250 mm in diameter drives a second pulley 1,000 mm in diameter by means of a belt as in Figure 3. The moment of inertia of the driven pulley is equal to 0.2 kg- m2. The belt connecting these pulleys is represented by two springs, each of stiffness k. For what value of k will the natural frequency be 6 Hz? r00000 0.2 50 mm 0 mm (b) Figure 3

The figure below shows a single degree of freedom control surface/actuator system. The control surface has a mass moment of inertia J = 30 kg.m2 about the hinge, the effective actuator stiffness and damping values are k = 3000 N/m and c = 500 Ns/m respectively and the rotation of the control surface is rad. The actuator lever arm has length a = 0.2 m. A force f (t) = 58 (t) N is applied to the control surface at a distance d = 1 m from the hinge. It is assumed that the main surface of the wing is fixed rigidly as shown in the figure. Assume small angle approximation. Determine the tip velocity (velocity at the location of f(t)) at t = 0.1 s 0(t) f(t) C 152.74 mm/s 499.47 mm/s 583.77 mm/s 400.63 mm/s 285.64 mm/s d

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Consider the following spring system. Assume down is the positive direction. Write the stiffness matrix A 188 Displacement www my SE (₂ • Compute the displacements caused by the external forces f with spring constants e E