Two simple harmonic motions are represented by the equations $x_{1}=5 \sin \left(2 \pi t+\frac{\pi}{4}\right), x_{2}=5 \sqrt{2}(\sin 2 \pi t+\cos 2 \pi t)$ The ratio of the amplitude of $x_{1}$ and $x_{2}$ is
AIIMS 2019, Medium
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The harmonic equations are given as,
$x_{1}=5 \sin \left(2 \pi t+\frac{\pi}{4}\right)$
$x_{2}=5 \sqrt{2}(\sin \pi t+\cos 2 \pi t)$
The amplitude are,
$A_{1}=5$
$A_{2}=\sqrt{(5 \sqrt{2})^{2}+(5 \sqrt{2})^{2}}=10$
The ratio of the amplitude is,
$\frac{A_{1}}{A_{2}}=\frac{5}{10}=1: 2$
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