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Equation 4.8 should be

$x(t)=\left(x_{0}-{\frac {\delta }{1-r^{2}}}\right)\cos \omega _{n}t+{\frac {{\dot {x}}_{0}}{\omega _{n}}}\sin \omega _{n}t+{\frac {\delta }{1-r^{2}}}\cos \omega t$

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