The equation should be:
d d t [ ξ 1 ξ 2 ξ 3 ξ 4 ] = [ ξ 2 1 m 1 ( − b 1 ξ 2 − k 1 ξ 1 + k 2 ξ 3 − k 2 ξ 1 + b 2 ξ 4 − b 2 ξ 2 ) ξ 4 1 m 2 ( − k 2 ξ 3 + k 2 ξ 1 − b 2 ξ 4 + b 4 ξ 2 ) ] {\displaystyle {\frac {d}{dt}}{\begin{bmatrix}\xi _{1}\\\xi _{2}\\\xi _{3}\\\xi _{4}\end{bmatrix}}={\begin{bmatrix}\xi _{2}\\{\frac {1}{m_{1}}}\left(-b_{1}\xi _{2}-k_{1}\xi _{1}+k_{2}\xi _{3}-k_{2}\xi _{1}+b_{2}\xi _{4}-b_{2}\xi _{2}\right)\\\xi _{4}\\{\frac {1}{m_{2}}}\left(-k_{2}\xi _{3}+k_{2}\xi _{1}-b_{2}\xi _{4}+b_{4}\xi _{2}\right)\end{bmatrix}}}
Return to errata.