For the spring$-$damper system shown below,$$

k$1=15$ N$/$m

k$2=12$ N$/$m

k$0=7$ N$/$m

m$1=1$ kg

m$2=3$ kg

q$1$ and q$2$ are displacements of masses m$1$ and m$2,$ respectively. A periodic force Q$2($t$)$ is applied to mass m$2$ as given in the graph, whereas no force is applied on mass m$1,$ that is Q$1($t$)=0.$

Obtain the steady$-$state displacements of the two masses using three methods given below and compare the results $($show one figure for q$1$ and another for q$2)$:

$($a$)$ Modal analysis,

$($b$)$ Matlab direct integration tools such as lsim or ode$45$ or your own Runge$-$Kutta algorithm, and

$($c$)$ NASTRAN or FEMAP