Hi Student,

In damped oscillation , amplitude goes on decaying exponentially, a = a0e^−bt where b = damping coefficient.
Initially, a0/3 = a0e^−b×100T, T=time of one oscillation
or 1/3 = e^−100bT ...(i)
Finally , a = a0e^−b×200T
or a = a0[e^−100bT]^2
or a = a0×[1/3]^2 ( From Eq. (i))
or a = a0/9

Feel free to ask doubts in the Comment Section.

I hope this information helps you.

Good Luck!