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# The purpose of this experiment is to see what factors affect the period of one complete oscillation of a simple pendulum.

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Introduction

SCIENCE COURSEWORK

PENDULUM EXPERIMENT

Aim

The purpose of this experiment is to see what factors affect the period of one complete oscillation of a simple pendulum.

In this investigation I am going to discover and investigate the factors, which affect the time for one complete oscillation of a simple pendulum. It is important to understand what a pendulum is. A pendulum has a weight or mass fixed and left hanging of the string. An oscillation is one cycle of the pendulums motion e.g. from position a to b and back to a. I will time how long it takes for one oscillation of the pendulum.

I am going to do a simple preliminary experiment to investigate which of the factors I test have an effect on the time for one complete oscillation. The factors basic variable factors I can test are:
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Length (the distance between the point of suspension and the mass)
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Mass (the weight in g of the item suspended from the fixed point)
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Swing size (the length I release the pendulum)

*The point of equilibrium is the point at which kinetic energy (KE) is the only force making the mass move and not gravitational potential energy (GPE).

I will test the extremes of these factors as I can assume that if they have any effect on the period of oscillation it will become obvious.

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 Length of string Swing size     40cm Time taken for 10 oscillations (sec) 60 40 17 60 40 17 50 40 16 50 40 16 40 40 15 40 40 15 30 40 14 30 40 14 20 40 12 20 40 12 10 40 10 10 40 10

I can see from the results that there is one clear factor, length and swing size. For mass the period for 10 oscillations does nothing to change the factor. The variation between the averages is small enough for me to conclude that these factors have a minimal effect if any on the period of an oscillation. From the information from this preliminary experiment I can now go onto investigate how precisely length effects the oscillation period of a pendulum. I have also learnt from this preliminary it is necessary for the clamp stand to be held firmly in place so it does not rock.

Scientific Theory

As a pendulum is released it falls using gravitational potential energy which can be calculated using mass (kg) x gravitational field strength (which on earth is 10 N/Kg) x height (m). As soon as the pendulum moves this becomes kinetic energy, which can be calculated using 1/2 x mass (kg) x velocity2 (m/s2) and gravitational potential energy. At the point of equilibrium the pendulum just uses kinetic energy and then it returns to kinetic energy and gravitational potential energy and finally when the pendulum reaches maximum rise it is just gravitational potential energy and this continues. From this I can deduce that  kinetic energy = gravitational potential energy. If these were the only forces acting on the pendulum it would go on swinging forever but the energy is gradually converted to heat energy by friction with the air (drag) and with the point the mass is hung from. The amplitude of the oscillation therefore decreases until eventually the pendulum comes to a rest at the point of equilibrium.

As the amplitude is increased so too is the gravitational potential energy because the height is increased which affects the gravitational potential energy and therefore the kinetic energy must also increase by the same amount. The pendulum then oscillates faster because height or distance is involved in v2 in the kinetic energy formula. However the pendulum has a larger distance to cover so they balance each other out and the period remains the same. The period is also the same if the amplitude is reduced.
For the mass as it is increased this affects both the gravitational potential energy and the kinetic energy as they both contain mass in their formulas but velocity is not affected. The formulas below show that mass can be cancelled out so it does not affect the velocity at all.
gravitational potential energy = kinetic energy
mgh = 1/2mv2

Length affects the period of a pendulum and I have found a formula to prove this and I will now attempt to explain it. The formula is:
T=period of one oscillation (seconds)
p=pi or p
l=length of pendulum (cm)
g=gravitational field strength (10m/s on earth)

This shows that the gravitational field strength and length both have an effect on the period. However although the 'g' on earth varies slightly depending on where you are as the experiments are all being done in the same place this will have no effect as a variable. Length is now the only variable. This means that T2 is directly proportional to length.
T2= 2plg

The distance between a and b is greater in the first pendulum. However the pendulum has gained no amplitude so therefore no additional gravitational potential energy or kinetic energy so it will still travel at the same speed. The first pendulum therefore has a greater distance to travel and at the same speed so it will have a greater period.
I can predict from this scientific knowledge that the period squared will be directly proportional to the length.

I will now change the mass to (10g) and see if the time for 10 oscillations varies.

 Length of string Swing size     25cm Time taken for 10 oscillations                 (sec) 60 25 16 60 25 16 50 25 15 50 25 15 40 25 14.5 40 25 14.5 30 25 13 30 25 13 20 25 12 20 25 12 10 25 10.5 10 25 10.5

Conclusion

The results obtained show that my experiment was successful for investigating how length effects the period of an oscillation because they are the same and agree with what I predicted would happen. The procedure used was not too bad because my results are very similar to what they would be under perfect circumstances. My results are reasonably accurate as they fulfil what I thought and said would happen. However there are a few minor anomalies which can be seen in the graphs and in the tables. They have a larger gap from what they should have been according to the formula than usual.

Evaluation

Most of the procedure was suitable because it gave a useful and relevant outcome but it could have been improved in a number of ways. Making the swing size more precise, making sure the string is taut when the pendulum is released and making the string the exact length it should to be could increase the reliability of the evidence. The anomalous results I have may be down to a number of reasons but could mainly be blamed on my releasing the pendulum and providing it with an external force, which would affect the period. My timing of the stopping and starting of the stopwatch could be inaccurate. The overall results may be a 1/100 of a second out because I used the gravitational field strength of 10 when the actual field strength may be different. If the above improvements were added in, the results would be more accurate and reliable.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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## Here's what a teacher thought of this essay

4 star(s)

This is a well written report that includes good science.
1. The background section and analysis contain excellent reasoning.
2. The prediction and evaluation are good.
3. The method for the preliminary test is well structured but unfocused.
4. The table of results could be better presented.
5. The beginning of the report lacks structure, there are many subheadings missing.
**** (4 stars)

Marked by teacher Luke Smithen 22/05/2013

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