The Factors Which Affect The Time For

One Full Oscillation Of A Pendulum Essay, Research Paper

An investigation on the factors affecting the period of one complete oscillation of a simple pendulum In this investigation I aim 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 simple pendulum is a weight or mass suspended from a fixed point and allowed to swing freely. An oscillation is one cycle of the pendulums motion e.g. From position a to b and back to a. The period of oscillation is the time required for the pendulum to complete one cycle of its motion. This is determined by measuring the time required for the pendulum to reoccupy a given position.

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:

. Length (the distance between the point of suspension and the mass)

. Mass (the weight in g of the item suspended from the fixed point)

. Angle (the angle between the point of equilibrium and the maximum point the pendulum reaches)

*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. To make sure my results are reliable and to allow for any anomalies I will repeat the experiment 4 times for each extreme. I will also keep all the other factors constant so if the results change for the different extremes I can be sure which factor is causing this change, as all the others will remain constant. To keep the results as accurate as possible I will measure the period of 10 oscillations and only use one decimal place to allow for my reaction time. Results Angle (º) Time Taken (sec) for 10 oscillations

90º 13·4 13·4 13·8 13·7 Average:13·6

45º 13·2 13·2 13·1 12·9 13·1

Length: 0·3m, Mass: 20g Mass (g) Time Taken (sec) for 10 oscillations

400g 11·1 11·3 11·3 11·4 Average:11·3

100g 11·6 11·1 11·0 11·2 11·2

Length: 0·2cm, Angle: 45º

Length (cm) Time Taken (sec) for 10 oscillations

0·25m 10·4 10·5 10·5 10·3 Average:10·4

0·65m 16·8 16·0 16·5 15·9 Average:16·3

Mass: 50g, Angle: 40º

I can see from the results that there is one clear factor, length. For Angle and mass the period for 10 oscillations is roughly the same for both of the extremes. 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 GPE 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 KE which can be calculated using 1/2 x mass (kg) x velocity2 (m/s2) and GPE. At the point of equilibrium the pendulum just uses KE and then it returns to KE and GPE and finally when the pendulum reaches maximum rise it is just GPE and this continues. From this I can deduce that KE = GPE. 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. From this I can now explain why the amplitude and the mass have no effect on the period of oscillation. As the amplitude is increased so too is the GPE because the height is increased which affects the GPE and therefore the KE must also increase by the same amount. The pendulum then oscillates faster because height or distance is involved in v2 in the KE 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 GPE and the KE 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.

GPE = KE

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 leng

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