Q 11-13-017NEETJEE MainMedium
The time taken by a particle in SHM of period $T$ to go from the extreme position to half the amplitude is
Answer: (C) $\dfrac{T}{6}$
Concept. From the extreme $x = A\cos\omega t$.
Step 1. Phase. $\cos\omega t = \dfrac12 \Rightarrow \omega t = \dfrac{\pi}{3}$.
Step 2. Time. $t = \dfrac{T}{6}$ (longer than $\dfrac{T}{12}$ from the mean, since the particle is slow near the extreme).
Answer. $\dfrac{T}{6}$ (Option C).
Solution by Sreeraj P, M.Sc Physics