What affects the time period of a pendulum.

What effects the time for one period?

When the bob is moved from equilibrium (The point of equilibrium is the point at which kinetic energy is the only force making the mass move and not gravitational potential energy) either left or right and then is released, it oscillates in a vertical plane in the shape of an arc of a circle. This is then reversed back to its starting position.

 

The weight pulling down on the pendulum bob causes the bob to accelerate towards its normal resting point. This acceleration can be calculated by the formula a = -gA. The angle size can also be linked to the arc length, this is shown in the formula, x = LA. With L being the length of the string. This leads us to the equation for acceleration of a simple pendulum bob a = -g/L x.  These two formulae then give us the formula for a period, this is

Where L = length of string from pivot to bob

           g = acceleration due to gravity

          T = time of period.

This tells me that there are only two variables, that I have direct control over, that can effect the period of the bob. These are the angle, and the length of the string. There is one other variable and that is the force of gravity; this could vary because the pull of gravity is not the same all over the earth.   

What will affect the accuracy of results?

Fair Testing

There are a few invariables mainly caused by human error that we should consider before conducting the experiment. These include:-

Clamp, string, measuring equipment, stopwatch, person who does all the measuring and timing, weights, position where knot is tied, angle where it is released (amplitude).

To make sure our results are accurate we need to keep everything but the variable constant. Below are some simple guidelines to ensure that our testing is fair.

Note: Although during my research I ascertained that the mass of the bob does not effect the period of the pendulum, I should still keep this constant, as I should only have one variable in my experiment.

Note: The friction on the string caused by the air will affect the results. Ideally, this experiment would be conducted in a vacuum. However, we have no equipment in school that we could use to achieve this. So, therefore we will have to conduct the experiment with the knowing that all are results will be slightly affected by the surrounding air atoms.

Safety

There are many accidents that could happen if this experiment was not carried out safely; below I have outlined a few simple guidelines to prevent such accidents occurring.

Apparatus

For our experiment we needed:

• A length of String
• A bob
• Clamp and retort stand
• A heavy mass
• A large protractor
• A Stopwatch
• A meter ruler
• Scissors

Method

1. Measure the string to the desired length
2. Place string on centre of bob
3. We then pulled the string back to 15 degrees
4. We then released the bob and started the stopwatch at the same time.
5. We let the bob swing backwards and forwards 10 times
6. We then stopped the pendulum swinging and recorded the times.
7. We repeated the experiment with the same length 3 times
8. We then repeated steps 1-6 for string lengths 10cm, 20cm 30cm, 40cm, 50cm

Diagram

Errors in Measuring/Judgment: In many cases we found that when we repeated the experiments, we found that the time or the amplitude was different. This was because every time we did it there was a margin or error. Nobody in the world could ever measure it and get it right with your bare hands. We therefore took the results by averaging the result from three repeated tests so that we won’t get one very strange result from one particular area. We could not measure very accurately either. Many times when a person measures it again, we found that it was often different by 1-3mm. So we will be comparing all results by showing the true time mathematically by the sum: T= 2π √(l/g).

Preliminary Work

To confirm that the theory’s are correct we performed some preliminary experiments using different variables.

With a small bob at 29 cm’s it come to 1.189 seconds for one swing. With a heavier bob it came to 1.207 seconds, so the weight doesn’t affect it, as proved in the theory. The difference between the previously mentioned results was because of unavoidable human error.

However with the small bob with a short string it took 0.929 seconds compared to the long string which took 1.207 seconds. So obviously the length of the string affects the time. The smaller the string the bob is attached to the smaller the time it takes for a swing.

We also investigated whether the angle the ball is dropped from affects the time. With a big angle it took 12.85 secs so their was no big difference.

My prediction, based on the preliminary work is that the smaller the string the bob is attached to the smaller the time it takes for one swing. In contrast, the larger the string is, the longer the bob takes for one oscillation.

Were using a retort stand and clamp to swing the pendulum from. We will measure time for 10 ,20 ,30 ,40 , 50, 60, 70, 80, 90 7 100 cm’s length strings.

We will get 3 measurements and then average the results.

For each result we will let the pendulum swing for 10 periods and then average to eliminate human error as much as possible.

The angle will be same that we drop it from, also the weight of the bob will be the same. Were using a protractor to keep the angle the same.

We will put weights on the stand to make the results accurate.

We will not be going over 15 for the angle.