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

• llauren84
In summary, the conversation discusses an experiment involving a simple pendulum where the maximum angle is increased in increments of 5 degrees while keeping the string length constant. The period of the pendulum seems to increase as the maximum angle increases, which raises the question of whether this is due to drag force or a mistake in the experiment. The individual wonders if the period should be the same for all maximum angles since it is dependent on the free fall acceleration and string length, but acknowledges the possibility of air resistance playing a role. The concept of small angle approximation is mentioned as a factor in the period being independent of amplitude. The individual also mentions being new to physics and seeking help. A resource for further reading is also provided.

#### 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!

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.)