This is a case of damped vibration as the amplitude of vibration is decreasing with time.
Amplitude of vibrations at any instant t is given by $a = a_0e^{–bt}$, where $a_0$ is the initial amplitude of vibrations and b is the damping constant.

Now, when t = 100T, $a = a_0/3$  [T is time period]

Let the amplitude be $a'$ at t = 200T.
i.e. after completing 200 oscillations.

$\therefore$ $a = a_0/3 = a0e^{–100Tb}$   ...(i)

and $a' = a_0e^{–200Tb}$ ...(ii)

From (i), ${1 \over 3} = {e^{ - 100Tb}}$
$\therefore$ ${e^{ - 200Tb}} = 1/9$

From (ii), $a' = {a_0} \times {1 \over 9} = {{{a_0}} \over 9}$

$\therefore$ The amplitude will be reduced to 1/9 of initial value.