Velocity & Acceleration in SHM question from MHT CET 2026 (15 Apr, Shift 1)

Answer: (b)

1. $|v| = \omega\sqrt{A^2 - x^2}$, $|a| = \omega^2 x$.
2. $\omega\sqrt{16 - 9} = \omega^2(3) \Rightarrow \omega = \frac{\sqrt{7}}{3}$ rad/s.
3. $T = \frac{2\pi}{\omega} = \frac{6\pi}{\sqrt{7}}$ s.
4. So the answer is (b) $\frac{6\pi}{\sqrt{7}}$ s.