$\mathrm{x}=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}\left[\frac{\mathrm{a}}{\mathrm{a}^{2}+\mathrm{b}^{2}} \sin \omega \mathrm{t}+\frac{1}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}} \cos \omega \mathrm{t}\right]$

$\mathrm{x}=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}[\cos \phi \sin \omega \mathrm{t}+\sin \phi \cos \omega \mathrm{t}]$

Let $\cos \phi=\frac{a}{\sqrt{a^{2}+b^{2}}}$

$\therefore \mathrm{x}_{2} \sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}} \sin (\omega \mathrm{t}+\phi)$ this is condition of $SHM$