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ME 3504_HW_no_4_2008

# ME 3504_HW_no_4_2008 - ME 3504 3rd ed In HW no 4 Vibrations...

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ME 3504 HW no. 4 Vibrations Dr. Kirk 3 rd ed. In [ ] See latest posted syllabus on course web page for due date. Syllabus Problem 1.84 + [1.95 +] The plus sign means the following: The equivalent car mass m, equivalent car stiffness k, and equivalent car damping c, are as specified in the text description of 1.84 [1.95]. Using the standard assumed form of solution for a SDOF as shown below, solve in terms of x o and v o , for the unknowns A and B. )} t sin( B ) t cos( A { e ) t ( x d d t n ω ω ζω + = (a) Then solve for the amplitude, R and phase, ψ of this equation if expressed as )} t cos( R { e ) t ( x d t n ψ ω ζω = Compare your result to Eq 1.38 on page 18 [24] of Inman. (b) Is the amplitude the same? (c) Is the phase the same? Why not? (d) Draw a sketch of the A and B components and indicate the angles ψ and φ . (e) Write a MATLAB m-file to plot this equation for the IC’s specified. Plot the result for 5 cycles of the damped period, T d . This is then Figure 1.

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