Q131 / 160 · AP EAMCET 2024 (22 May Shift 1) · Physics
Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t+\frac{\pi}{4}\right]$. The ratio of their amplitudes is
- A$1: 1$
- Correct answerB$2: 1$
- C$1: 3$
- D$\sqrt{3}: 1$
Solution
$\begin{aligned}
& \text { } \mathrm{y}_1=5[\sin 2 \pi \mathrm{t}+\sqrt{3} \cos 2 \pi \mathrm{t}] \\
& \mathrm{y}_2=5 \sin \left[2 \pi \mathrm{t}+\frac{\pi}{4}\right]
\end{aligned}$
$\therefore \quad$ Ratio of amplitudes,
$\frac{\mathrm{A}_1}{\mathrm{~A}_2}=\frac{5 \times \sqrt{(1)^2+(\sqrt{3})^2}}{5}=\frac{2}{1}=2: 1$
Hence, the correct answer is option: 'B'.