Two $SHM$ are represented by equations, $y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)\,,{y_2} = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$
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$y_{1}=6 \cos \left(6 \pi t+\frac{\pi}{6}\right)$
$y_{2}=3(\sqrt{2} \sin 3 \pi t+\cos 3 \pi t)$
$=6\left[\frac{\sqrt{3}}{2} \sin 3 \pi t+\frac{1}{2} \cos 3 \pi t\right]$
$6\left[\sin \left(3 \pi t+\frac{\pi}{3}\right)\right]$
$=6 \sin \left(3 \pi t+\frac{\pi}{3}\right)$
ratio of their amplitude is $1 .$
Hence,
Option $A$ is correct answer.
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