matlab code please. A horizontal earthquake oscillation F$($t$)=$F$0$cos$\backslash$omega t

affects each floor of a five$-$floor building. In the case of

a single$-$floor building, the center$-$of$-$mass position x$($t$)$

of the building satisfies mx$+$kx$=$E where the natural

frequency of the building is $/.$ The earthquake

force E is given by Newton$$s second law: E$($t$)=-$mF$($t$).$

If $\backslash$omega $/,$ then the amplitude of x$($t$)$ is large compared to the amplitude of the force E; a smallamplitude earthquake wave can resonate with the building and possibly demolish the structure.

The following assumptions and symbols are used to quantify the oscillation of the five$-$floor

building.

$$ Each floor is considered a point mass located at its center$-$of$-$mass. The floors have

masses m$1,$ m$2,...,$ m$5.$

$$ Each floor is restored to its equilibrium position by a linear restoring force or Hooke$$s

force. The Hooke$$s constants are k$1,$ k$2,...,$ k$5.$

$$ The locations of masses representing the five floors are x$1,$ x$2,...,$ x$5.$ The equilibrium

position is x$1=$ x$2=...$x$5=0.$

$$ Damping effects of the floors are ignored and a frictionless system is assumed.

The differential equations for the model are obtained via the Newton$$s second law. This results in

the following system, where k$6=0,$ Ej$=-$mjF$$ for j$=1,2,3,4,5$ and F$=$F$0$cos$\backslash$omega t$.$