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If a simple pendulum has Significant amplitude (up to a factor of \( 1 / \mathrm{e} \) of original) only in the period between \( t=0 \) s to \( t=\tau s \), then \( \tau \) may be called the average life of the pendulum. When the spherical bob
\( P \) 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) \( \frac{1}{b} \)
(B) \( \frac{2}{\mathrm{~b}} \)
(C) \( \frac{0.693}{\mathrm{~b}} \)
(D) \( b \)
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