If a simple pendulum has significant amplitude (upto a factor of \(1 / e\) of original) only in the period between \(t = 0s\) 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 the small) in seconds