कोई कण सरल आवर्त गति करता है जिसका आवर्तकाल \(2\) सेकण्ड है। इस कण द्वारा अपनी माध्य स्थिति से अपने आयाम की आधी दूरी के विस्थापन में लगा समय \(\frac{1}{ a } s\) है। यहाँ \('a'\) का मान निकटतम पूर्णांक में \(\dots\) होगा।

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.