A spring mass system is executing simple harmonic motion. The equation of  motion is given by  $y=8\sin \omega t+6\cos \omega t$. The amplitude of the resultant is

$$\begin{gathered} resul\tan t amplitude=R=\sqrt{a^2+b^2+2ab\cos \varphi } \\ here a, b are amplitudes, \varnothing is phase difference \end{gathered}$$

The given equation can be written as  $y=8\sin \omega t+6\sin \left(\omega t+\frac{\pi }{2}\right)$
Here $\varphi =\frac{\pi }{2}$; a=8; b=6, substitute

$$\begin{gathered} R=\sqrt{8^2+6^2+\left(2\times 8\times 6\cos \frac{\pi }{2}\right)} \\ R=\sqrt{8^2+6^2} \\ R=\sqrt{64+36} \\ R=\sqrt{100}=10units \end{gathered}$$