Given the two degree of freedom system in Fig. P4.2, complete the following. (a) Write the equations

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Given the two degree of freedom system in Fig. P4.2, complete the following.

(a) Write the equations of motion in matrix form.
(b) Write the system characteristic equation using Laplace notation. Your solution should be a polynomial that is quadratic in \(s^{2}\) with appropriate numerical coefficients.
(c) Calculate the natural frequencies (in \(\mathrm{Hz}\) ).
(d) Determine the two mode shapes (normalize to coordinate \(x_{1}\) ).

image text in transcribed

Fig. P4.2 Two degree of freedom spring-mass system.

image text in transcribed

Fig. P4.3 Two degree of freedom spring-mass system

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Mechanical Vibrations Modeling And Measurement

ISBN: 119669

1st Edition

Authors: Tony L. Schmitz , K. Scott Smith

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