If two S.H.M are represented by equations $Y_{1} = 10 \sin [3 π t + \frac{π}{4}]$ and $Y_{2} = 5 [\sin (3 πt) + \sqrt{3} \cos (3 πt)]$ . The ratio of their amplitudes is

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2 : 1

1 : 2

1 : 1

$1 : \sqrt{2}$

answer is C.

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Detailed Solution

$Y_{1} = 10 \sin [3 π t + \frac{π}{4}]$

$Y_{2} = 5 [\sin (3 πt) + \sqrt{3} \cos (3 πt)]$

$= 10 [\frac{1}{2} \sin 3 πt + \frac{\sqrt{3}}{2} \cos 3 πt]$

$= 10 \sin (3 πt + \frac{π}{3})$

$∴ A_{1} : A_{2} = 1 : 1$

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