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 = τ s, then τ 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:
Text Solution
Verified by ExpertsD
here b is damping coefficient; gk¡ b
This has solution of type
x = eλt substituting this
mλ 2 + bλ + k = 0
λ = 
on solving for x, we get
x = 
a cos (ꞷ 1 t – α)
ꞷ 1 = 
where ꞷ 0 = 
So, average life = 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems