A particle oscillates in straight line simple harmonically with period 8 second and amplitude \(4 \sqrt{2} \mathrm{~m}\). Particle starts from mean position. The ratio of the distance travelled by it in \(1^{\text {st }}\) second of its motion to that in \(2^{\text {nd }}\) second is \(\left(\sin 45^{\circ}=1 / \sqrt{2}, \sin \frac{\pi}{2}=1\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.