6. What are the eigenvectors and natural frequencies for the system illustrated in Fig. 5? Note that the
x? and x? coordinates reflect relative motion of the mass, not absolute motion. The unstretched
length of each of the three springs is $l$, $k_3 = 1000$ N/m, $k_2 = 2000$ N/m, $k_1 = 1000$ N/m, $m_3 = 0.1$ kg,
$m_2 = 0.1$ kg, $m_1 = 0.1$ kg.