Question:
Two simple harmonic motions are represented by the equations
$\mathrm{x}_{1}=5 \sin \left(2 \pi \mathrm{t}+\frac{\pi}{4}\right)$ and $\mathrm{x}_{2}=5 \sqrt{2}(\sin 2 \pi \mathrm{t}+\cos 2 \pi \mathrm{t})$
The amplitude of second motion is times the amplitude in first motion.
Solution:
$\mathrm{x}_{2}=5 \sqrt{2}\left(\frac{1}{\sqrt{2}} \sin 2 \pi \mathrm{t}+\frac{1}{\sqrt{2}} \cos 2 \pi \mathrm{t}\right) \sqrt{2}$
$=10 \sin \left(2 \pi t+\frac{\pi}{4}\right)$
$\therefore \frac{\mathrm{A}_{2}}{\mathrm{~A}_{1}}=\frac{10}{5}=2$
Ans. 2
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