If a simple pendulum has significant amplitude (upto a factor of 1/e of original ) only in the period between t = 0 to t = ζ then ζ 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 (assuming damping is small ) in second is [ AIEEE 2012]​

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