Fair test
To make sure this is a fair test I will:
- Try to create as little friction as possible where the string is attached to the clamp.
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Let go with out adding any extra forces.
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Kept the string taut.
- Make sure the mass and swing size remain the same in each test in case they have a small effect on the results.
- Keep the whole experiment in the same place so that the gravitational field strength does not change.
To make this a safe experiment:
- The clamp should stand secure same with the G-clamp.
- Laboratory procedures should be followed.
RESULTS
*The mass of the bob for these experiments is (35g)
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.
I can see from the results that there is one clear factor, length and swing size again. For mass the period for 10 oscillations does nothing to change the factor again. I also noticed that the shorter the string and lighter the mass the faster the pendulum travels. The longer the string and lighter the mass it takes a few seconds more but the longer the string and heavier the mass it’s a bit faster.
Scientific Theory
From my results I have found out that the period squared is as predicted directly proportional to the length of the pendulum because my graph is a straight line and goes through 0. The graph with period plotted against length also provides the useful information that period and length have a relationship, which involves the indice 2. I have noticed the pattern that if you divide the period squared of the pendulum by the length of the pendulum you get roughly the same figure.
I can draw a conclusion from my evidence that the formula:
This is correct because if you rearrange it to form T2= 2pl this fits perfectly
with the graph and my results. If you remove the constants from the formula you are left with a direct link from T2 to l. As the length increases the period goes up in smaller and smaller amounts, which again agrees with the formula. These results totally support my original prediction and they also support the scientific theory. The shape of the graph immediately shows this.
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.
