Velocity & Acceleration in SHM question from MHT CET 2024 (9 May, Shift 2)

Answer: (c)

1. $\frac{V_1^2}{\omega^2} = A^2 - x_1^2$ and $\frac{V_2^2}{\omega^2} = A^2 - x_2^2$.
2. Divide: $V_1^2(A^2 - x_2^2) = V_2^2(A^2 - x_1^2)$.
3. $A^2(V_1^2 - V_2^2) = V_1^2x_2^2 - V_2^2x_1^2$.
4. $A = \sqrt{\frac{V_1^2x_2^2 - V_2^2x_1^2}{V_1^2 - V_2^2}}$, so the answer is (c).