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Two SHMs are represented by the equations $large {y_1}, = ,10sin left( {3pi t + frac{pi }{4}} right),,and,,{y_2}, = ,5left[ {sin 3pi t + sqrt 3 cos 3pi t} right]$ . Their amplitudes are in the ratio

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1:2

2:1

1:3

1 :1

answer is D.

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Detailed Solution

$large {y_1}, = ,10sin left[ {3pi t + frac{pi }{4}} right]$

$large {y_2}, = ,5sin left[ {(3pi t) + sqrt 3 ,cos 3pi t} right]$

$large , = ,5 times 2left[ {frac{1}{2}sin 3pi t + frac{{sqrt 3 }}{2}cos 3pi t} right]$

$large , = 10left[ {cos 60.sin 3pi t + sin {{60}^0}.cos 3pi t} right]$

$large {y_2}, = ,10sin left( {3pi t + {{60}^o}} right);,,{y_1}, = ,10sin left( {3pi t + frac{pi }{3}} right)$

Ratio of amplitudes = $large frac{{10}}{{10}}, = ,frac{1}{1}$

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