Analysis of Experiment

Analysis - Inclusion of drag forces in a model

Derivation of equation 9.3

    (9.3)
The force balance on the bob involves inertia, gravitation, and drag forces as in the case of the skydiver. Thus we can start with equation (3.1).
    (3.1)
where mass of the bob, kg
           drag coefficient of the bob, Ns2/m2

The initial condition is represented by the first experimental point taken at t=t0. Thus

  m/s   (9.1)

Separating variables in equation (3.1) we obtain

Multiplying each side of the equation by k/m and including the initial condition as the lower limit of integration.

Integrating we obtain

Rearranging the equation
Taking the of both sides of the equation
and

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