STANDARD Physics Simple Harmonic Motion MCQ Question

To find the ratio of the amplitudes of the two simple harmonic motions, we first identify the amplitudes from their equations. For $y_1 = 10\sin\left(\frac{\pi}{4}(12t + 1)\right)$, the amplitude is 10. For $y_2 = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t)$, we can rewrite it in the form $R\sin(3\pi t + \phi)$, where $R = \sqrt{5^2 + (\sqrt{3} \cdot 5)^2} = 10$. Thus, both motions have an amplitude of 10, giving a ratio of 10:10 or 1:1. Other options are incorrect as they suggest different ratios that do not reflect the calculated amplitudes.