Two SHM are represented by equations, y_1 = 6 ( 6 t + 6 ) ,, y_2 = 3 ( 3 3 t + 3 t )

Two SHM are represented by equations, y_1 = 6 ( 6 t + 6 ) ,, y_2 …

MCQ

Two $SHM$ are represented by equations, $y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)\,,{y_2} = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$

✓
ratio of their amplitudes is $1$
B
ratio of their time periods is $1$
C
ratio of their maximum velocities is $1$
D
ratio of their maximum acceleration is $1$

✓

Answer

Correct option: A.

ratio of their amplitudes is $1$

a
$y_{1}=6 \cos \left(6 \pi t+\frac{\pi}{6}\right)$

$y_{2}=3(\sqrt{2} \sin 3 \pi t+\cos 3 \pi t)$

$=6\left[\frac{\sqrt{3}}{2} \sin 3 \pi t+\frac{1}{2} \cos 3 \pi t\right]$

$6\left[\sin \left(3 \pi t+\frac{\pi}{3}\right)\right]$

$=6 \sin \left(3 \pi t+\frac{\pi}{3}\right)$

ratio of their amplitude is $1 .$

Hence,

Option $A$ is correct answer.

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