Two simple harmonic motions are represented by the equations x _ … - Vidyadip

MCQ

Two simple harmonic motions are represented by the equations

${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ and ${x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})$

The amplitude of second motion is ....... times the amplitude in first motion.

A
$8$
✓
$2$
C
$10$
D
$5$

✓

Answer

Correct option: B.

$2$

b
${x}_{2}=5 \sqrt{2}\left(\frac{1}{\sqrt{2}} \sin 2 \pi {t}+\frac{1}{\sqrt{2}} \cos 2 \pi {t}\right) \sqrt{2}$

$=10 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$

$\therefore \frac{{A}_{2}}{{A}_{1}}=\frac{10}{5}=2$

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