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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 stoke`s law is valid, and the ratio of coefficient of viscosity of air to that of carbon dioxide is 1 : 3, the time in which the amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide will be close to ? (ln 5 = 1.601, ln 2 = 0.693)

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 stoke`s law is valid, and the ratio of coefficient of viscosity of air to that of carbon dioxide is 1 : 3, the time in which the amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide will be close to ? (ln 5 = 1.601, ln 2 = 0.693)

Grade:12

1 Answers

Aryaman Agrawal
13 Points
6 years ago
This is a case of damped oscillation. 
Equation x=Ae^(-bt/2m)
where b is directly proportional to viscosity. 
Let b/2m=k
Then, x=Ae^(-kt)
put x=8 and A=10 to form equation 1.
x=5 and A=10 to form equation 2.
solve for t. Answer will come around 161.5s

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