Consider the system of Problem 2.15, repeated here as Figure P2.36 with the effects of damping indicated. The physical constants are J = 25 kg m² , k = 2000 Nm/rad, and the applied moment is 5 Nm at 1.432 Hz acting through the distance r = 0.5 m. Compute the magnitude of the steady-state response if the measured damping ratio of the spring system is ζ = 0.01. Compare this to the response for the case where the damping is not modeled (ζ = 0).

Problem 2.15

An airfoil is mounted in a wind tunnel for the purpose of studying the aerodynamic properties of the airfoil’s shape. A simple model of this is illustrated in Figure P2.15 as a rigid inertial body mounted on a rotational spring fixed to the floor with a rigid support. Find a design relationship for the spring stiffness, k, in terms of the rotational inertia, J; the magnitude of the applied moment, M₀ ; and the driving frequency, ω, that will keep the magnitude of the angular deflection less then 5°. Assume that the initial conditions are zero and that the driving frequency is such that ω_n2 - ω² > 0