If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between $t = Os$ to $ t = \tau s$, then $\tau$ 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 of proportionality, the average life time of the pendulum is ( assuming damping is small ) in seconds :
