The amplitude of SHM $\mathrm{y}=2\left(\sin 5\mathrm{\pi t}+\sqrt{2}\cos \mathrm{\pi t}\right)$ is

The equation of SHM is $$\begin{gathered} \mathrm{y}=\mathrm{A} \sin \left(\mathrm{\omega t}+\mathrm{\varphi }\right) \mathrm{or} \mathrm{y}=\mathrm{A}\left(\sin \mathrm{\omega tcos} \mathrm{\varphi }+\cos \mathrm{\omega t} \mathrm{sin\varphi }\right)....\left(\mathrm{i}\right) \\ \mathrm{The} \mathrm{given} \mathrm{expression} \mathrm{is} \mathrm{y}=2\left(\sin 5\mathrm{\pi t}+\sqrt{2}\cos \mathrm{\pi t}\right) ...\left(\mathrm{ii}\right) \\ \mathrm{Acos\varphi }=2 \mathrm{and} \mathrm{Asin\varphi }=2\sqrt{2} \\ \mathrm{Squaring} \mathrm{and} \mathrm{adding}, \mathrm{we} \mathrm{get} \mathrm{A}=2\sqrt{3} \end{gathered}$$