Damped Oscillations

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

If a simple pendulum has significant amplitude (up to a factor of $\frac{1}{e}$ of original) only in the period between $t=0$ to$\mathit{ }t=\mathrm{\tau }$, then $\mathrm{\tau }$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with $b$ as the constant proportionality, the average lifetime of the pendulum in (assuming damping is small) in seconds$:$

When a damped harmonic oscillator completes $100$ oscillations, its amplitude is reduced to ${\left(\frac{1}{3}\right)}^{\mathrm{rd}}$ of its initial value. What will be its amplitude when it completes $200$ oscillations?