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Two simple harmonic motions are represented as $y_1=10 \sin \omega t$ and $y_2=10 \sin \omega t+5 \cos \omega t$. The ratio of the amplitudes of $y_1$ and $y_2$ is
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The correct answer is:
$2: \sqrt{5}$
Given, $Y_1=10 \sin \omega t$ and
$Y_2=10 \sin \omega t+5 \cos \omega t$
Amplitude of $Y_1$ and $A_1=10$
Amplitude of $Y_2$ is $A_2=\sqrt{(10)^2+(5)^2}=5 \sqrt{5}$
Thus, $\frac{A_1}{A_2}=\frac{10}{5 \sqrt{5}}=2: \sqrt{5}$
$Y_2=10 \sin \omega t+5 \cos \omega t$
Amplitude of $Y_1$ and $A_1=10$
Amplitude of $Y_2$ is $A_2=\sqrt{(10)^2+(5)^2}=5 \sqrt{5}$
Thus, $\frac{A_1}{A_2}=\frac{10}{5 \sqrt{5}}=2: \sqrt{5}$
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