How Does Mass and Pivot Position Affect a Compound Pendulum's Period?

[chriswalker]

Homework Statement

I am doing some coursework investigating a simple compound pendulum (in the form of a meter stick with holes drilled along it's length) and the effect of different variables on it's time period.

I am using a stopclock to measure the time taken for 15 variations to minimise error when finding time period. I am also using a rotary potentiometer to allow for comparisons between results.

Variables include:

1) Pivot point fixed at the top of the pendulum, in the first hole. I am then using a 100g mass and moving this along the length of the pendulum (in each different drilled hole) to see the effect on the time period.

2) Keeping the pivot point at the same place as before, I am varying the mass from 50g to 400g at the bottom hole of the pendulum.

3) Keeping the mass in the bottom hole of the pendulum, I am moving the pivot point down the pendulum.

Homework Equations

Erm I know them but new to this so don't know how to write them out. I think the main equation is time period = 2 x pi times the square root of inertia over mass of pendulum times grav times distance from centre of mass to suspension point.

The Attempt at a Solution

Basically two probs.

In the first experiment I got basically an intial fall in the time period then steady rise as I moved the 100g down away from the pivot point down the meter stick. Can somebody explain the theory in how this happened, as I am a young student and am experiencing severe difficulties...

In the second experiment, with the mass at the bottom, when changing the mass from 50g to 400g the time period increased. My teacher had said that this was not to be expected. Could someone please help me in explaining this behaviour?

Any help would be much appreciated.

 

[Doc Al]

I assume you took the mass & rotational inertia of the stick into consideration.

For each of your experimental trials, what were your values for I, m, and L? And your expected period?

 

[Moetasim]

Hello, it's great to hear that you are conducting an investigation on a simple compound pendulum! Let me try to explain the theory behind the results you observed in your experiments.

For the first experiment, where you moved the 100g mass along the length of the pendulum, the time period initially decreased and then increased as you moved the mass away from the pivot point. This is because the time period of a simple pendulum is affected by its length. As you moved the mass down the pendulum, you were effectively increasing the length of the pendulum, which results in a longer time period. However, when the mass is close to the pivot point, it has less distance to travel and therefore the time period decreases. This is known as the "pendulum length effect" and is a well-known phenomenon in pendulum experiments.

For the second experiment, where you varied the mass at the bottom of the pendulum, it is expected that the time period would increase as the mass increases. This is because the time period of a simple pendulum is also affected by its mass. As you increase the mass, you are also increasing the inertia of the pendulum, which results in a longer time period. Your teacher might have been referring to the fact that the time period did not increase proportionally to the increase in mass. This could be due to other factors such as friction or air resistance, which can affect the accuracy of your results.

I hope this helps to clarify the theory behind your results. Keep up the good work in your investigations!