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 \(x_{1}\) ).

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

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

Transcribed Image Text:

+3 k = 1105 N/m /// Ix k2=6x105 m2=2 m = 3 kg