The equation should be:
x(t)=x˙0+x0ωn(ζ+ζ2−1)2ωnζ2−1e(−ζωn+ωnζ2−1)t−x˙0−x0ωn(−ζ+ζ2−1)2ωnζ2−1e(−ζωn−ωnζ2−1)t.
Return to errata.