b
In damped oscillation, amplitude goes on decaying exponentially, \(a=a_{0} e^{-b t}\) where \(b =\) damping coefficient.

Initially \(, \frac{a_{0}}{3}=a_{0} e^{-b \times 100 T}, \mathrm{T}=\) time of one oscillation or \(\frac{1}{3}=e^{-100 b T} \ldots(i)\)

Finally, \(a=a_{0} e^{-b \times 200 T}\)

or \(a=a_{0}\left[e^{-100 b T}\right]^{2}\)

or \(a=a_{0} \times\left[\frac{1}{3}\right]^{2} \quad[\text { From Eq. (i) }]\)

or \(a=a_{0} / 9\)