The motion of a particle as per $x=Asin \omega t + Bcos\omega t$ is :-
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$\mathrm{x}=\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}$
$x=\sqrt{A^{2}+B}\left[\frac{A}{A^{2}+B^{2}} \sin \omega t+\frac{B}{\sqrt{A^{2}+B^{2}}} \cos \omega t\right]$
$\mathrm{x}=\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}[\cos \phi \sin \omega \mathrm{t}+\sin \phi \cos \omega \mathrm{t}]$
$\mathrm{x}=\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}} \sin (\omega \mathrm{t}+\phi)$
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