AIIMS 2018 Physics Simple Harmonic Motion MCQ Question

To find the amplitude $A$ in simple harmonic motion, we use the formula for total mechanical energy $E = \frac{1}{2} k A^2$. Rearranging this gives $A = \sqrt{\frac{2E}{k}}$. Substituting the given values $E = 4 \, \text{J}$ and $k = 800 \, \text{N/m}$ results in $A = \sqrt{\frac{2 \times 4}{800}} = \sqrt{\frac{8}{800}} = \sqrt{0.01} = 0.1 \, \text{m}$, which is not listed among the options, making option D correct as it indicates that none of the provided answers are valid. The other options are irrelevant since they do not provide any numerical values or calculations related to the problem.