If a simple pendulum has significant amplitude (up to a factor of `(1)/(e)` of orginal) only in the period between `t = 0` sec to `t = tau` sec, then `tau` may be called the average life of 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:

Options

A. b
B. `(1)/(b)`
C. `(2)/(b)`
D. `(0.693)/(b)`

Answer

C