$\left[\begin{array}{c}{i}_1\\ v_1\\ x_2\\ v_2^{}\end{array}\right]=\left[\begin{array}{ccccc}0& 1& 0& 0& ?\\ -\frac{k_1+k_2}{M_1}& -\frac{B_1{B}_2}{M_1}& \frac{k_1}{{}_1}& \frac{B_2}{{}_1}& ?\\ 0& 0& 0& 1& ?\\ \frac{k_2}{M_2}& \frac{B_2}{M_2}& -\frac{k_2}{M_2}& -\frac{B_2}{M_2}& ?\end{array}\right]\left[\begin{array}{c}{x}_1\\ v_1\\ x_1\\ x_2\\ v_2\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ \frac{1}{M_2}\end{array}\right][gradF]$I$)$ Initial conditions: when t $=0,$ x $2=1,$ v $1=-1,$ v $2=1,$ x $1=-1.$

II$)$ Time span: t $=0$ to $25$s$.$

III$)$ Consider M $1=1,$ M $2=2,$ B $1=2,$ B $2=1,$ K $1=1,$ K$2=2,$ and f$=0.$

Write a Matlab code using the $$initial$$ command to find the system response:y$1=$v$1$; y$2=$k$2$x$2$

with the given initial conditions.

The general matrix that is needed for this problem has been solved as below