Q 11-13-123JEE MainJEE Main 2021 (27 Aug, Shift 2)Easy
Two simple harmonic motions are represented by the equations $y_1 = 10\sin\left(3\pi t + \frac{\pi}{3}\right)$; $y_2 = 5\left(\sin3\pi t + \sqrt{3}\cos3\pi t\right)$. Ratio of amplitude of $y_1$ to $y_2 = x : 1$. The value of $x$ is
Numerical value type. Enter your answer.
Answer: 1
$\sin3\pi t + \sqrt{3}\cos3\pi t = 2\sin\left(3\pi t + \frac{\pi}{3}\right)$, so $y_2 = 10\sin\left(3\pi t + \frac{\pi}{3}\right)$.
Both amplitudes are $10$: $x = 1$.
Solution by Sreeraj P, M.Sc Physics