Investigating the Relationship Between Max Theta and Period in a Simple Pendulum

[llauren84]

I am working on my lab report for the simple pendulum and we did an experiment where we increased the max theta in increments of 5 degrees, while keeping the length of the sting the same. We started from 5 degrees and went to 45 degrees. For some reason the periods seem to increase slighty as we increase the max theta. I am just wondering if this is due to the drag force or if it our mistake. I think that we should have the same period independent of the angle because we were told that T=2π √(L/g) and even proved this. Since the period, T is dependent on the free fall accelleration and the length of the string, which does not change throughout our experiment, shouldn't the period for all max angles be the same? I am guessing that air resistance comes into play, but I am not sure how. We haven't learned that yet and since this is my first physics class ever and I am very stumped. Thanks for your help!

 

[Doc Al]

The period of a simple pendulum is independent of amplitude for small amplitudes. Recall that the derivation of the pendulum formula uses the small angle approximation sinθ ≈ θ (radian measure, of course). As the amplitude increases, you'll get a greater period. (And I suppose air resistance will have a greater effect as well.)

Read this: http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.html"

 

[llauren84]

Thanks so much!