\( f_{i} \) particle of mass \( 200 \mathrm{~g} \) is making SHM un...

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\( f_{i} \) particle of mass \( 200 \mathrm{~g} \) is making SHM under the influence of a spring of force constant \( k=90 \mathrm{~N} / \mathrm{m} \) and a damping
\( \mathrm{P} \) constant \( b=40 \mathrm{~g} / \mathrm{s} \). Calculate the time elapsed for the W amplitude to drop to half its initial value (Given \( \ell n(1 / 2)=-0.693 \) ) [AMU (Engg.) 2012; NCERT Exemplar]
(a) \( 7 \mathrm{~s} \)
(b) \( 9 \mathrm{~s} \)
(c) \( 4 \mathrm{~s} \)
(d) \( 11 \mathrm{~s} \)
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