An Investigation to See Which Factors Affect the Swinging Of a Pendulum

• Hypothesis:  I don’t think the angle of the arc will affect the time.
• Procedure:  We will test the time a 80g weight attached to a string takes to swing and return to its original position, whilst measuring the arc at different angles . We will time how long it takes for the pendulum to travel through the air and return to the starting point with an arc of 10 degrees. After we record the data, we will change the angle.  We will repeat this process five times.

Exp 3

Changing angle (variable)

Mass = 80g

Length = 0.3 (30cm)

These results show me that the angle of the arc does not affect the time for the pendulum to swing.

What My Preliminary Work has Shown Me

My preliminary work has now shown me that the only affecting factor in this investigation in the length of the string. Therefore, this variable will be the only one I will be using in my final investigation. After completing three experiments, I concluded that the only factor affecting the time of the swing of a pendulum was the length of the string. The hypothesis for Experiment 1 was correct, as was the hypothesis for both experiments 2 and 3, the weight on the string, and the angle of the arc.  The time increased as the length of the string increased.  The following graph shows how the length of the string (the independent variable) affects the time (the dependent variable).  

Diagram

Key Factors Identified

Apparatus:

• Meter ruler
• Protractor
• Clamp stand
• G-clamp
• Stop clock
• String
• Mass

Plan

Due to my preliminary work, I have found out that the length of the string is the only affecting factor in this investigation. Therefore, that will be my only variable. In order to find out how length of the string affects the swinging of a pendulum, I will take a result from six different lengths. They will be: 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 metres. For each experiment, I will repeat each length 3 times. Therefore, I will be doing a total of 18 experiments. Instead of just timing one swing, I have decided to time 10 swings. I have also decided to repeat each experiment 3 times. Once I have done this, I will then find the average for 10 swings and then the average for 1 swing. This is to try and reduce any possibilities of error, such as my reaction time etc. This is how I will record each length:

• I will set up all my equipment

• I will attach my string to my clamp stand

• I will measure the designated length for my string, cut it and attach the weight

• I will use the protractor to line up the 5o angle, whilst keeping the string taut  

• I will carefully drop the pendulum, ensuring it swings back and forth, and not in a circular motion. At the same time, my partner will start the stop clock

• After 10 swings, I will stop the stop clock and record my result

• I will repeat again twice, so that I will have done the same experiment 3 times

• I will remove the string and measure it for the next experiment

• I will repeat the steps until I have done all six experiments, all 3 times each.

Fair Test

In order to keep the investigation fair and accurate, we need to distinguish which factors of the test will be variables and which will be kept constant.

Variables & Constants

In this experiment, there are 2 constants, mass and angle. There is one variable, which is the length of the string.

There are various steps I have gone to, to ensure that the investigation is as fair as possible.

• Instead of just timing one swing, I have decided to time 10 swings.
• I have decided to repeat each experiment 3 times.
• I will use the same stop clock throughout. I need to do this, because different stop clocks may be faster or slower than other ones
• The mass will be a constant of 80g throughout the experiment
• Angle of arc shall be a constant of 5 degrees. This will ensure
  that there is no variation of the forces acting on the pendulum.
• The intervals between the string lengths will increase by 10cm each
  time. This will help me to identify a clear pattern in my results.
• To ensure that the velocity is not affected, I will ensure that there are no
  obstructions to the swing of the pendulum.
  

However, even with all these precautions in place, the chances of error are very high in this investigation. It is a very unreliable investigation. Infact, it is practically impossible to do this experiment perfectly. This is because there are many things which will affect the recording of the results. These are:

• The time it takes for the eye to react to the pendulum swinging
• The time it takes for the thumb to react, and press the button on the stop clock
• Any random winds that could blow the pendulum
• The length could be a millimetre out
• The rounding of the time to 2 decimal places
• The string could move in a circular motion, rather than back and forth
• The arc measurements could be a millimetre out
• The stop clock could be to quick or slow
• Air resistance slowing the pendulum down

Safety

In order to ensure the investigation is done safely, we need to:

• Not throw the pendulum, just let it go of it
• Make sure the mass is tied securely to the string, so it doesn’t come lose and fly out at somebody
• Carry the weights safely, so you don’t drop them
• Clear the area before you start to swing the pendulum
• Care will be taken not to let the bob come into contact with anything
  whilst swinging the pendulum, as the weight is relatively heavy (80g)
• Excessively large swings will be avoided (angle of arc will be 5
  degrees

Prediction

Because the pendulum uses simple harmonic motion, I predict that the longer the string, the longer time it takes for the pendulum to make 1 full swing. Therefore, the length of the string is directly proportional to the time taken for the pendulum to swing. This is because as I increase the length of the string, the arc increases with it. This means that it will have further to travel, consequently taking more time to make 1 full swing.

I also predict that my results will be a straight line on a graph. This is because of the formula.

The formula for the pendulum swinging is:

T = 2π√L/G

In this formula:

T= time – It is a variable

2π√*/G = It is a constant

L= length – It is a variable

In the straight line formula:

Y = MX

So:

Y = Variable

M = Constant

X = Variable

Therefore, on the graph there will be a straight line. This is because the straight line formula, Y = MX when broken down is a variable = constant x variable. The same pattern can be seen in the formula for a swinging pendulum.

Results Table

Results Graphs

The following graphs show how the length of the string (the independent variable) affects the time (the dependent variable).  

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Analysis of Results

All my graphs and my results table show that my prediction was correct. The graphs clearly show a smooth curve with a positive gradient. This indicates that as the length of the
pendulum is increased, the period will increase. I predicted that the longer the string, the longer time it takes for the pendulum to make 1 full swing, and also that the length of the string is directly proportional to the time taken for the pendulum to swing. This is because as I increase the length of the string, the arc increases with it. This means that it will have further to travel, consequently taking more time to make 1 full swing.

I also predicted that my results will be a straight line on a graph. This was also correct. I proved this by explaining that:

The formula for the pendulum swinging is:

T = 2π√L/G

In this formula:

T= time – It is a variable

2π√*/G = It is a constant

L= length – It is a variable

In the straight line formula:

Y = MX

So:

Y = Variable

M = Constant

X = Variable

Therefore, on the graph there will be a straight line. This is because the straight line formula, Y = MX when broken down is a variable = constant x variable. The same pattern can be seen in the formula for a swinging pendulum.

However, even though my results were correct, they were no where near perfect. During my experiment, I realised that there were many errors that I have probably made, due to general reaction time etc. Realising that fact, I did try to minimise as many errors as possible. These were the measures I took:

• I timed how long it took for 10 swings, to minimise the reaction time my eyes and thumb used to react
• I repeated each experiment 3 times, to check that my results were normal
• I used the same stop clock throughout, to ensure it was the same speed for each experiment

Evaluation

In my opinion, I think that my experiments went well. There were few anomalous results, and my prediction was correct.  However, I do not think this is a very good experiment. This is because there are too many errors that can, and will be made. This is mostly due to the time it takes for the eye and thumb to react, and the millimetre errors that occur when measuring the string and the arc. 

Factors which may have affected the accuracy of my results include:

• Error in measurement of angle of arc. This angle proved difficult to
  measure and it was hard to get the exact same angle for each result. To
  improve the accuracy of this measurement, I could have attached the protractor to the clamp stand so that it was in a fixed position.
• Error in measurement of string. To improve the accuracy of this, I
  could have marked off the points with a pen to ensure they were as
  accurately measured as possible.
• Human reaction time. Depending on human reaction time, the
  measurement period time could have been measured inaccurately, due
  to slow reactions when setting the stop-clock etc. This could have been
  improved by involving another person to aid me with my experiment
  for a quicker reaction time.

In my opinion, if I had to do this experiment again, I would use a computerised pendulum, such as the one which can be found on ‘the pendulum lab’ on the internet. This website has a virtual pendulum, which has the exact measurements for length of string and angle of the arc. This will eliminate any human errors, which will give a more accurate result.

The procedure was relatively reliable, excluding human error, and so I can conclude that my evidence is sufficient to support a firm conclusion that:

The only factor which affects the period of a simple pendulum is its
length. As the length increases, so does the period.