# Time period in different medium

1 vote
45 views

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from
10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601,ln 2 = 0.693).

I could not understand anything in it . Can anyone provide some hints .

we have an equation $A= A_0 e^{-bt/2m}$
$F _{damping } = - bv$ where b is damping coefficient.
so on solving , we get $\lambda = b/2m$
substitute $\lambda$ in first equation and then take ratios as already shown.