The equation should be:
x ( t ) = x ˙ 0 + x 0 ω n ( ζ + ζ 2 − 1 ) 2 ω n ζ 2 − 1 e ( − ζ ω n + ω n ζ 2 − 1 ) t − x ˙ 0 − x 0 ω n ( − ζ + ζ 2 − 1 ) 2 ω n ζ 2 − 1 e ( − ζ ω n − ω n ζ 2 − 1 ) t . {\displaystyle x(t)={\frac {{\dot {x}}_{0}+x_{0}\omega _{n}\left(\zeta +{\sqrt {\zeta ^{2}-1}}\right)}{2\omega _{n}{\sqrt {\zeta ^{2}-1}}}}e^{\left(-\zeta \omega _{n}+\omega _{n}{\sqrt {\zeta ^{2}-1}}\right)t}-{\frac {{\dot {x}}_{0}-x_{0}\omega _{n}\left(-\zeta +{\sqrt {\zeta ^{2}-1}}\right)}{2\omega _{n}{\sqrt {\zeta ^{2}-1}}}}e^{\left(-\zeta \omega _{n}-\omega _{n}{\sqrt {\zeta ^{2}-1}}\right)t}.}
Return to errata.
