If a simple pendulum has Significant amplitude (up to a factor of 1/ e of original) only in the period between t = 0s to t = ts, then t 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:
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a = –bv
hence v = v0 e–bt
comparing with N = N0e–lt
Average life time