Engineering
Physics
Damped Oscillation
Question

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:

 0.693b

 2b

b

 1b

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Solution

a = –bv

hence v = v0 e–bt

comparing with N = N0e–lt

Average life time  =1λ=1b