If a simple pendulum has significant amplitude (up to a factor of \...

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If a simple pendulum has significant amplitude (up to a factor of \( 1 / e \) of original) only in the period between \( t=0 \) s to \( t=\tau \) s, then \( \tau \) may be called the average life of the
\( \mathrm{P} \) pendulum. When the spherical bob of the pendulum suffers

W 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 seconds is
[AIEEE 2012]
(a) \( 0.693 / b \)
(b) \( b \)
(c) \( 1 / b \)
(d) \( 2 / b \)
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