Energy in SHM question from MHT CET 2024 (15 May, Shift 1)

Answer: (b)

1. $K = 75\%$ of $E$ means $U = 25\%$ of $E$: $\frac{x^2}{A^2} = \frac{1}{4} \Rightarrow x = \frac{A}{2}$.
2. $x = A\sin\omega t \Rightarrow \sin\omega t = \frac{1}{2} \Rightarrow \omega t = \frac{\pi}{6}$.
3. $t = \frac{\pi/6}{2\pi/T} = \frac{T}{12}$
4. So the answer is (b) $\frac{T}{12}$.