If a simple pendulum has significant amplitude (up to a factor of1//e of original) only in the period between `t-0s to t=tau s`, then `tau` may be called the average life of the pendulum. When the sphetical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with b as the constant of propotional to average life time of the pendulum is (assuming damping is small) in seconds:

Options

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

Answer

D

Explanation

For damped motion, angular displacement may be written as,
`theta=theta_(0)e^(-btau/2) sin(omegat+theta)`
:. Angular amplitude `=theta_(0)e^(-(btau)/2)`
Hence, `theta_(0)/e=theta_(0)e^(-(btau)/2)`
`1=(btau)/2`
`tau=2/b`