A) \[\frac{{{a}_{0}}}{2}\]
B) \[\frac{{{a}_{0}}}{6}\]
C) \[\frac{{{a}_{0}}}{12}\]
D) \[\frac{{{a}_{0}}}{4}\]
E) \[\frac{{{a}_{0}}}{9}\]
Correct Answer: E
Solution :
In damped oscillation, amplitude goes on decaying exponentially \[a={{a}_{0}}{{e}^{-bt}}\] where\[b=\]damping coefficient. Initially, \[\frac{{{a}_{0}}}{3}={{a}_{0}}{{e}^{-b\times 100T}}\] where T is time of one oscillation. Or \[\frac{1}{3}={{e}^{-100bT}}\] ?.. (i) Finally, \[a={{a}_{0}}{{e}^{-b\times 200T}}\] Or \[a={{a}_{0}}{{[{{e}^{-100bT}}]}^{2}}\] Or \[a={{a}_{0}}\times {{\left[ \frac{1}{3} \right]}^{2}}\] [from Eq.(i)] Or \[a=\frac{{{a}_{0}}}{9}\]
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