A) \[2\times 3\]
B) \[{{2}^{2}}\]
C) \[{{2}^{3}}\]
D) \[3\times {{2}^{2}}\]
Correct Answer: C
Solution :
The variation in amplitude of a damped harmonic oscillator with time is given by: \[A={{A}_{0}}{{e}^{-bt}}\] \[{{A}_{0}}=\] initial amplitude, b = damping factor It is given that after 1 min. \[{{A}_{1}}={{A}_{0}}/2={{A}_{0}}{{e}^{-bt}}\] \[\therefore 2={{e}^{b}}\] \[\therefore \]After 3 min. \[{{A}_{3}}={{A}_{0}}/x={{A}_{0}}{{e}^{-3b}}\] \[\therefore x={{e}^{3b}}={{2}^{3}}\]
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