Chapter 9.6, Problem 20E

For the coupled mas-spring system governed by system (10), assume $m_1=m_2=1\text{ kg,}$ $k_1=k_2=k_3=1\text{ N/m}$, and assume initially that $x_1\left(0\right)=0\text{ m, }{x^{\prime }}_1\left(0\right)=0\text{m}/\text{sec},x_2\left(0\right)=2\text{ m}$ and ${x^{\prime }}_2\left(0\right)=0\text{m}/\sec$. Using matrix algebra techniques solve this initial value problem.

$\begin{array}{l}{m}_1{x^{″}}_1=-k_1{x}_1+k_2(x_2-x_1),(10)\\ m_2{x}_2{}^o=2k_2(x_2-x_1)-k_3{x}_2,\end{array}$