The $S.H.M.$ of a particle is given by the equations $=2 \sin \omega t+4 \cos \omega t$. Its amplitude of oscillation is ........ units
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(d)
$x=2 \sin \omega t+4 \cos \omega t$
It can also be written as
$x=\sqrt{2^2+4^2}\left(\frac{2}{\sqrt{2^2+4^2}} \sin \omega t \frac{4}{\sqrt{2^2+4^2}} \cos \omega t\right)$
$x=\sqrt{20} \sin (\omega t+\phi)$
$\sqrt{20}=\text { Amplitude }$
$\text { or Amplitude }=2 \sqrt{5}$
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