Which of the following statements regarding the damping force of a damped oscillator is $NOT$ correct?

$A$ block of mass $m$ is connected to a light spring of force constant $k$. The system is placed inside a damping medium of damping constant $b$. The instantaneous values of displacement,acceleration and energy of the block are $x, a$ and $E$ respectively. The initial amplitude of oscillation is $A$ and $\omega^{\prime}$ is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

When an oscillator completes $100$ oscillations,its amplitude is reduced to $\frac{1}{3}$ of its initial value. What will be its amplitude after it completes $200$ oscillations?

The mechanical energy of a damped oscillator becomes half of its initial energy in $4 \ s$. In another $t \ s$,its mechanical energy becomes $12.5 \%$ of its initial mechanical energy. Then $t=$ (in $s$)

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 \ s$. In another $10 \ s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals

$A$ particle is performing simple harmonic motion. If the oscillations are damped oscillations,then the angular frequency is given by: