Two simple harmonic motion, are represented by the equations y _ … - Vidyadip

MCQ

Two simple harmonic motion, are represented by the equations ${y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)$

$y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$

Ratio of amplitude of ${y}_{1}$ to ${y}_{2}={x}: 1$. The value of ${x}$ is ...... .

A
$2$
✓
$1$
C
$3$
D
$4$

✓

Answer

Correct option: B.

$1$

b
${y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right) \Rightarrow \text { Amplitude }=10$

${y}_{2}=5(\sin 3 \pi {t}+\sqrt{3} \cos 3 \pi {t})$

${y}_{2}=10\left(\frac{1}{2} \sin 3 \pi {t}+\frac{\sqrt{3}}{2} \cos 3 \pi {t}\right)$

${y}_{2}=10\left(\cos \frac{\pi}{3} \sin 3 \pi {t}+\sin \frac{\pi}{3} \cos 3 \pi {t}\right)$

${y}_{2}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right) \Rightarrow \text { Amplitude }=10$

So ratio of amplitudes $=\frac{10}{10}=1$

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