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Just a nobody
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In my intro mechanics lab class, we did an experiment where we measured how much energy was lost in a pendulum over 300 seconds. In my case, the final energy of the pendulum was 2.4% what the initial energy was.
The pendulum was constructed by attaching a cylindrical metal bob to a thread.
Today I tried to simulate that system using a computer. I came up with this equation of motion:
[itex]\ddot{\theta} = - \frac{g}{l} \sin \theta - \frac{1}{2m} C_D \rho A l \frac{\dot{\theta}^3}{|\dot{\theta}|}[/itex]
Where the last term is due to the air resistance on the bob:
[itex]F_D = \frac{1}{2} C_D \rho A v^2[/itex]
I estimated the drag coefficient [itex]C_D[/itex] to be somewhere between 0.5 and 1, based on the values I saw in the figure in the top right of http://en.wikipedia.org/wiki/Drag_coefficient" .
When I ran the simulation, the final energy/initial energy ratio turned out to be 33%, even taking [itex]C_D[/itex] to be my maximum estimated value, 1. So what I'm wondering is: what other sources of energy loss might there be that I'm not thinking of? I realize that I'll never be able to get the exact value, but I should be able to get something closer to 2.4% than 33% is.
I attached the program (it's in C) in case anyone cares to take a look. If you have gcc, you can compile with `gcc -o pendulum -lm pendulum.c` and run with `./pendulum`.
The pendulum was constructed by attaching a cylindrical metal bob to a thread.
Today I tried to simulate that system using a computer. I came up with this equation of motion:
[itex]\ddot{\theta} = - \frac{g}{l} \sin \theta - \frac{1}{2m} C_D \rho A l \frac{\dot{\theta}^3}{|\dot{\theta}|}[/itex]
Where the last term is due to the air resistance on the bob:
[itex]F_D = \frac{1}{2} C_D \rho A v^2[/itex]
I estimated the drag coefficient [itex]C_D[/itex] to be somewhere between 0.5 and 1, based on the values I saw in the figure in the top right of http://en.wikipedia.org/wiki/Drag_coefficient" .
When I ran the simulation, the final energy/initial energy ratio turned out to be 33%, even taking [itex]C_D[/itex] to be my maximum estimated value, 1. So what I'm wondering is: what other sources of energy loss might there be that I'm not thinking of? I realize that I'll never be able to get the exact value, but I should be able to get something closer to 2.4% than 33% is.
I attached the program (it's in C) in case anyone cares to take a look. If you have gcc, you can compile with `gcc -o pendulum -lm pendulum.c` and run with `./pendulum`.
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