Is it possible to find the drag coefficient of a pendulum bob from the damping caused on it during swinging. I will be able to measure its displacement from the point of origin and plot it against time. I know the $F_D=\frac 12 \rho v^2AC_D$ equation could be used if I had more information, but I only have displacement from origin over time.
closed as off-topic by Jon Custer, Chair, Chris, stafusa, ZeroTheHero Oct 23 '18 at 15:15
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Welcome to the stack exchange! Good question.
But since there are losses other than drag you'll need to run two sets of tests:
- Pendulum swing in the air and
- Pendulum swing in a vacuum
To be as precise as possible you should use the nonlinear model (differential equation) of a pendulum
derived here which applies to the pendulum in vacuum, and without losses that might occur in whatever is suspending the pendulum.
The hard part at this point is determining a functional model that accounts for the non-drag energy losses. But assume you can do this - perhaps by trial and error - by proposing a loss model and fitting to data.
In any event this gives you the drag-free model.
You'll then need to modify this drag free model (which assumes a point mass) with a tangential force that's equal to the drag force on the projected area, $A$
$\rho$ is your calculated or measured air density , $v$ is the tangential velocity, and $C_D$ is the drag coefficient of the bob - what you are trying to solve for.
This gives you a total loss model
Between the measurements in vacuum and air, and the total and drag-free loss models you can back out, calculate $C_D$