Motion of a Pendulum in the Wind

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This Demonstration models the behavior of a simple pendulum subject to an additional force from air flow.

Contributed by: Erik Mahieu (November 2011)
Open content licensed under CC BY-NC-SA

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It is assumed that for air speeds less than 30 m/sec, the flow is nonturbulent and the drag force on the bob can be expressed as follows: , where

is the dimensionless drag coefficient; it depends on the geometry of the bob (0.47 is the accepted value for a sphere),

is the density of air (1.293 ),

is the cross-sectional area exposed to the air flow , and

is the air flow speed (m/sec).

Then the equilibrium of the forces acting on the bob becomes:

, with and .

Reducing this to the one degree of freedom of the system for , this gives the following equation of motion: .


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