The following mass$-$and$-$spring system has stiffness matrix K$.$ For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation.

$m_1=1,m_2=3$;$k_1=2,k_2=3,k_3=6$

Let ${}_1<msub><mrow><mi></mi></mrow><mrow><mn>2</mn></mrow></msub>$ be the two natural frequencies.

${}_1=\sqrt[\phantom{2}]{2}$

${}_2=2\sqrt[\phantom{2}]{3}$

$($Type exact answers, using radicals as needed.$)$