A) \[2\times 3\]
B) \[{{2}^{3}}\]
C) \[{{3}^{2}}\]
D) \[3\times {{2}^{2}}\]
Correct Answer: B
Solution :
Amplitude of damped oscillator \[A={{A}_{0}}{{e}^{-\lambda t}};\ \lambda \ =\]constant, t = time For t =1 min. \[\frac{{{A}_{0}}}{2}={{A}_{0}}{{e}^{-\lambda t}}\Rightarrow {{e}^{\lambda }}=2\] For t = 3 min. \[A={{A}_{0}}{{e}^{-\lambda \times 3}}=\frac{{{A}_{0}}}{{{({{e}^{\lambda }})}^{3}}}=\frac{{{A}_{0}}}{{{2}^{3}}}\] \[\Rightarrow X={{2}^{3}}\]
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