The equation should be
ξ(t)=c1([0ωn10ωn1]cosωn1t+[1010]sinωn1t)+c2([0ωn10ωn1]sinωn1t−[1010]cosωn1t)+c3([0−ωn20ωn2]cosωn2t+[−1010]sinωn2t)+c4([0−ωn10ωn2]sinωn2t+[10−10]cosωn2t).
Return to errata.