If a simple pendulum has Significant amplitude

If a simple pendulum has Significant amplitude (up to a factor of $1 /$ e of original) only in the period between $t=0 \mathrm{~s}$ to $\mathrm{t}=\tau \mathrm{s}$, then $\tau$ may be called the average life ofthe pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with " $b$ ' as the constant of proportionality, the average lifetime ofthe pendulum is (assuming damping is small) in seconds: