# HW5_Assg - Mechanical Vibrations Homework#5 Due 5Nov04...

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Mechanical Vibrations Homework #5 Due: 5Nov04 - Start of Class Part 1: Use the following parameters for all problems: m = 3 Kg, I G = 4 Kg meters 2 , k 1 = k 2 = 200 N/meter, r = 2 meters, f 1 ( t ) = F o cos Ω t . Also, you should use a coordinate system with x ( t ) and θ ( t ). 1. Derive the equations of motion for the system shown in Figure 1. Add in the assumption of proportional damping with modal damping ratios of ζ 1 = 0 . 01 and ζ 2 = 0 . 02. Show how to decouple the equations of motion into modal coordinates ( ) and solve for the transient motions of the system (in modal coordinates) using the following initial conditions and parameters: F o = 0, x (0) = π , ˙ x (0) = 0, θ (0) = π , ˙ θ (0) = 0. Convert the solutions back into physical coordinates and plot the transient motion of the system (i.e. use x ( t ) and θ ( t ) coordinates for graphing). k 1 x(t) m k 2 I G r f1(t) Figure 1: A two degree of freedom system with translation and rotation. 2. Find the expressions the transfer functions

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## This note was uploaded on 08/22/2011 for the course EML 4220 taught by Professor Chen during the Spring '08 term at University of Florida.

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HW5_Assg - Mechanical Vibrations Homework#5 Due 5Nov04...

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