Problem $2(30$ points$)$:

For a $2-$DOF system, as shown in Figure $2,$ with $m_1=m,m_2=2m,k_1=k,k_2=2k,$ and $c_1=c_2=0$ :

$1-$ The forcing term can be expressed as $F_1(t)=F_{0}cos(t)$ and $F_2(t)=2F_{0}cos(t),$ determine the value of ${}_1$ for which $x_1(t)=0,$ and ${}_2$ for which $x_2(t)=0.$

Figure $2$