# hw04 - 0 kg r 1 = i j k m v 1 = 7 i m s m 2 = 1 0 kg r 2 =...

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AE 352: Aerospace Dynamics II, Fall 2008 Homework 4 Due Friday, September 26 Problem 1. Consider a mass resting on the ﬂoor, and attached to a wall with a spring and damper. Let m = 4, k = 4, c = 1. A force F acts on the particle. (Note this is a 1D problem) (a) Find the equations of motion for this system. (b) Find the undamped natural frequency ω , and the damping ratio ζ . (c) Find the free (a.k.a. complementary) solution of this system. Is the system underdamped, critically damped, or overdamped? Plot the solution (i.e. plot x vs t ). (d) Let F = F 0 cos(3 t ). Find the steady state solution driven by this forcing. (e) Let F = F 0 cos( ω t ). Plot the ampliﬁcation factor versus frequency, as in Figure 3-19 in Greenwood. What is the resonant frequency ω R ? Problem 2. Problem 4.4 in Greenwood. Problem 3. Consider the following system of particles: m 1 = 2 .
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Unformatted text preview: 0 kg r 1 = i + j + k m v 1 = 7 i m / s m 2 = 1 . 0 kg r 2 = 4 j + 3 k m v 2 =-6 j m / s m 3 = 1 . 5 kg r 3 = 2 i + 2 k m v 3 =-3 i m / s m 4 = . 5 kg r 4 = 4 k m v 4 = 12 i + 5 k m / s (a) Find the center of mass of the system of particles at the instant described above. (b) Find the linear momentum of the system of particles at the instant described above. (c) Find the angular momentum of the system of particles about the origin at the instant described above. (d) Find the angular momentum of the system of particles about the center of mass at the instant described above. (e) If gravitational forces are the only forces acting on the system, what can you say about the future motion of the system? What quantities will be conserved? Page 1 of 1...
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