Question: Given the two degree of freedom system shown in Fig. P4.3, complete the following. (a) Write the equations of motion in matrix form. (b) Write

Given the two degree of freedom system shown in Fig. P4.3, 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) Determine the natural frequencies (in $\mathrm{rad} / \mathrm{s}$ ).
(d) Determine the mode shapes (normalize to coordinate $x_{2}$ ).

k X1 m X2 m

Fig. P4.4 Two degree of freedom spring-mass system.

k X1 m X2 m

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