forced harmonic vibration

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in page 51,3.1.10

the equation

$$\ddot{x}+2\zeta\omega_{n}\dot{x}+\omega_{n}^{2}x=\frac{F_{0}}{m}\sin\omega t $$

solved as
$$x(t)=\frac{F_{0}}{k}\frac{\sin(\omega t-\phi)}{\sqrt{[1-\left(\frac{\omega}{\omega_{n}}\right)^{2}]+[2\zeta\frac{\omega}{\omega_{n}}]^{2}}}+X_{1}e^{-\zeta\omega_{n}t}\sin\left(\sqrt{1-\zeta^{2}}\omega_{n}t+\phi_{1}\right) $$