Q 11-13-121JEE MainJEE Main 2021 (26 Aug, Shift 2)Easy
Two simple harmonic motions are represented by the equations $x_1 = 5\sin\left(2\pi t + \frac{\pi}{4}\right)$ and $x_2 = 5\sqrt{2}(\sin2\pi t + \cos2\pi t)$. The amplitude of the second motion is ______ times the amplitude in the first motion.
Numerical value type. Enter your answer.
Answer: 2
$\sin2\pi t + \cos2\pi t = \sqrt{2}\sin\left(2\pi t + \frac{\pi}{4}\right)$, so
$$x_2 = 5\sqrt{2}\cdot\sqrt{2}\sin\left(2\pi t + \frac{\pi}{4}\right) = 10\sin\left(2\pi t + \frac{\pi}{4}\right)$$
Amplitude ratio $= \dfrac{10}{5} = 2$.
Solution by Sreeraj P, M.Sc Physics