For the system shown in the figure;

a$)$ Determine the natural frequencies and mode shapes

b$)$ Obtain the responses ${}_1(t)$ and ${}_2(t)$ for

${}_1(0)=0^0$;${}_2(0)=5^0$ and ${}_1^{}(0)=0$;${}_2^{}(0)=4ra\frac{d}{s}$

$l_1=0\mathrm{.}4m,l_2=0\mathrm{.}5m,m_1=1kg,m_2=2kg$