One Full Oscillation Of A Pendulum Essay, Research Paper

An probe on the factors impacting the period of one complete oscillation of a simple pendulum In this probe I aim to detect and look into the factors which affect the clip for one complete oscillation of a simple pendulum. It is of import 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 rhythm of the pendulums gesture e.g. From place a to B and back to a. The period of oscillation is the clip required for the pendulum to finish one rhythm of its gesture. This is determined by mensurating the clip required for the pendulum to reoccupy a given place.

I am traveling to make a simple preliminary experiment to look into which of the factors I test have an consequence on the clip for one complete oscillation. The factors basic variable factors I can prove are:

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

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

? Angle ( the angle between the point of equilibrium and the maximal point the pendulum reaches )

*The point of equilibrium is the point at which kinetic energy ( KE ) is the lone force doing the mass move and non gravitative possible energy ( GPE ) .

I will prove the extremes of these factors as I can presume that if they have any consequence on the period of oscillation it will go obvious. To do certain my consequences are dependable and to let for any anomalousnesss I will reiterate the experiment 4 times for each extreme. I will besides maintain all the other factors constant so if the consequences alteration for the different extremes I can be certain which factor is doing this alteration, as all the others will stay changeless. To maintain the consequences every bit accurate as possible I will mensurate the period of 10 oscillations and merely utilize one denary topographic point to let for my reaction clip. Consequences Angle ( & # 186 ; ) Time Taken ( sec ) for 10 oscillations

90 & # 186 ; 13 & # 183 ; 4 13 & # 183 ; 4 13 & # 183 ; 8 13 & # 183 ; 7 Average:13 & # 183 ; 6

45 & # 186 ; 13 & # 183 ; 2 13 & # 183 ; 2 13 & # 183 ; 1 12 & # 183 ; 9 13 & # 183 ; 1

Length: 0 & # 183 ; 3m, Mass: 20g Mass ( g ) Time Taken ( sec ) for 10 oscillations

400g 11 & # 183 ; 1 11 & # 183 ; 3 11 & # 183 ; 3 11 & # 183 ; 4 Average:11 & # 183 ; 3

100g 11 & # 183 ; 6 11 & # 183 ; 1 11 & # 183 ; 0 11 & # 183 ; 2 11 & # 183 ; 2

Length: 0 & # 183 ; 2cm, Angle: 45 & # 186 ;

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

0 & # 183 ; 25m 10 & # 183 ; 4 10 & # 183 ; 5 10 & # 183 ; 5 10 & # 183 ; 3 Average:10 & # 183 ; 4

0 & # 183 ; 65m 16 & # 183 ; 8 16 & # 183 ; 0 16 & # 183 ; 5 15 & # 183 ; 9 Average:16 & # 183 ; 3

Mass: 50g, Angle: 40 & # 186 ;

I can see from the consequences that there is one clear factor, length. For Angle and mass the period for 10 oscillations is approximately the same for both of the extremes. The fluctuation between the norms is little plenty for me to reason that these factors have a minimum consequence if any on the period of an oscillation. From the information from this preliminary experiment I can now travel onto look into how precisely length effects the oscillation period of a pendulum. I have besides learnt from this preliminary it is necessary for the clinch base to be held steadfastly in topographic point so it does non sway. Scientific Theory

As a pendulum is released it falls utilizing GPE which can be calculated utilizing mass ( kilogram ) x gravitative field strength ( which on Earth is 10 N/Kg ) ten tallness ( m ) . Equally shortly as the pendulum moves this becomes KE which can be calculated utilizing 1/2 ten mass ( kilogram ) ten velocity2 ( m/s2 ) and GPE. At the point of equilibrium the pendulum merely uses KE and so it returns to KE and GPE and eventually when the pendulum reaches maximal rise it is merely GPE and this continues. From this I can infer that KE = GPE. If these were the lone forces moving on the pendulum it would travel on singing everlastingly but the energy is bit by bit converted to heat energy by clash with the air ( retarding force ) and with the point the mass is hung from. The amplitude of the oscillation therefore decreases until finally the pendulum comes to a remainder at the point of equilibrium. From this I can now explicate why the amplitude and the mass have no consequence on the period of oscillation. As the amplitude is increased so excessively is the GPE because the tallness is increased which affects the GPE and hence the KE must besides increase by the same sum. The pendulum so oscillates faster because tallness or distance is involved in v2 in the KE expression. However the pendulum has a larger distance to cover so they balance each other out and the period remains the same. The period is besides 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 expressions but speed is non affected. The expression below show that mass can be cancelled out so it does non impact the speed at all.

GPE = KE

mgh = 1/2mv2 Length affects the period of a pendulum and I have found a expression to turn out this and I will now try to explicate it. The expression is:

T=period of one oscillation ( seconds )

p=pi or P

l=length of pendulum ( centimeter )

g=gravitational field strength ( 10m/s on Earth ) This shows that the gravitative field strength and length both have an consequence on the period. However although the & # 8216 ; g & # 8217 ; on Earth varies somewhat depending on where you are as the experiments are all being done in the same topographic point this will hold no consequence as a variable. Length is now the lone variable. This means that T2 is straight relative to length.

T2= 2pl

g

The distance between a and B is greater in the first pendulum. However the pendulum has gained no amplitude so hence no extra GPE or KE so it will still go at the same velocity. The first pendulum therefore has a greater distance to go and at the same velocity so it will hold a greater period.

I can foretell from this scientific cognition that the period squared will be straight relative to the length. Apparatus:

? Stopwatch

? Weights

? Ruler

? Protractor

? G-clamp

? Clamp base

? Stringing

Method: The setup was set up as shown above. The amplitude was ever 45 & # 186 ; and the mass 10g. I held the twine taut and started the stop watch when I released the pendulum ; I so stopped the stop watch after the 10th oscillation. I used a scope of 10cm to 100cm to utilize a suited Ra

nge of measurings. I besides repeated each length 4 times to do the norm gained more dependable and to let for any anomalousnesss. To do the consequences more accurate I besides counted 10 oscillations intending if you divide the period by ten your reaction clip, which affects the length of the period, is reduced by 9/10. To do certain this was as just a trial as possible I:

? Tried to make as small clash as possible where the twine is attached to the clinch.

? Let travel with out adding any excess forces

? Kept the twine taut

? Made sure the mass and angle remain the same in instance they have a little consequence on the period.

? Keep the whole experiment in the same topographic point so that the gravitative field strength does non alter

To do this a safe experiment:

? No weight above 400g

? No angles above 90 & # 186 ;

? The clinch base is unafraid Consequences:

A Table to demo the periodic clip for 10 oscillations for assorted lengths Periodic clip ( seconds )

Length ( m )

0 & # 183 ; 1 6 & # 183 ; 1 6 & # 183 ; 1 6 & # 183 ; 1 6 & # 183 ; 0 Average periodic clip: 6 & # 183 ; 08

0 & # 183 ; 2 8 & # 183 ; 6 8 & # 183 ; 7 8 & # 183 ; 6 8 & # 183 ; 7 Average periodic clip: 8 & # 183 ; 65

0 & # 183 ; 3 10 & # 183 ; 2 10 & # 183 ; 3 10 & # 183 ; 3 10 & # 183 ; 3 Average periodic clip: 10 & # 183 ; 28

0 & # 183 ; 4 12 & # 183 ; 6 12 & # 183 ; 4 12 & # 183 ; 6 12 & # 183 ; 3 Average periodic clip: 12 & # 183 ; 48

0 & # 183 ; 5 14 & # 183 ; 0 14 & # 183 ; 1 13 & # 183 ; 9 13 & # 183 ; 8 Average periodic clip: 13 & # 183 ; 95

0 & # 183 ; 6 15 & # 183 ; 2 15 & # 183 ; 3 15 & # 183 ; 3 15 & # 183 ; 3 Average periodic clip: 15 & # 183 ; 28

0 & # 183 ; 7 16 & # 183 ; 4 16 & # 183 ; 4 16 & # 183 ; 5 16 & # 183 ; 6 Average periodic clip: 16 & # 183 ; 48

0 & # 183 ; 8 17 & # 183 ; 8 17 & # 183 ; 6 17 & # 183 ; 5 17 & # 183 ; 7 Average periodic clip: 17 & # 183 ; 65

0 & # 183 ; 9 18 & # 183 ; 8 18 & # 183 ; 5 18 & # 183 ; 4 18 & # 183 ; 8 Average periodic clip: 18 & # 183 ; 63

1 & # 183 ; 0 19 & # 183 ; 6 19 & # 183 ; 3 19 & # 183 ; 3 19 & # 183 ; 3 Average periodic clip: 19 & # 183 ; 38

Angle: 45 & # 176 ; , Mass:10g

To happen the mean period of one oscillation I must split my norm for 10 oscillations by 10.

A tabular array to demo the period of one oscillation for assorted lengths

Length Period Period harmonizing to expression

0 & # 183 ; 1 0 & # 183 ; 61 0 & # 183 ; 63

0 & # 183 ; 2 0 & # 183 ; 87 0 & # 183 ; 89

0 & # 183 ; 3 1 & # 183 ; 03 1 & # 183 ; 09

0 & # 183 ; 4 1 & # 183 ; 25 1 & # 183 ; 26

0 & # 183 ; 5 1 & # 183 ; 40 1 & # 183 ; 40

0 & # 183 ; 6 1 & # 183 ; 53 1 & # 183 ; 54

0 & # 183 ; 7 1 & # 183 ; 65 1 & # 183 ; 66

0 & # 183 ; 8 1 & # 183 ; 77 1 & # 183 ; 78

0 & # 183 ; 9 1 & # 183 ; 86 1 & # 183 ; 88

1 & # 183 ; 0 1 & # 183 ; 93 1 & # 183 ; 99 I am now traveling to make a tabular array by rearranging the expression I found so length is straight relative to the period of oscillation squared. A tabular array to demo the period squared for assorted lengths Length Period squared Period squared harmonizing to expression

0 & # 183 ; 1 0 & # 183 ; 37 0 & # 183 ; 40

0 & # 183 ; 2 0 & # 183 ; 76 0 & # 183 ; 79

0 & # 183 ; 3 1 & # 183 ; 06 1 & # 183 ; 19

0 & # 183 ; 4 1 & # 183 ; 56 1 & # 183 ; 59

0 & # 183 ; 5 1 & # 183 ; 96 1 & # 183 ; 96

0 & # 183 ; 6 2 & # 183 ; 34 2 & # 183 ; 37

0 & # 183 ; 7 2 & # 183 ; 72 2 & # 183 ; 76

0 & # 183 ; 8 3 & # 183 ; 13 3 & # 183 ; 17

0 & # 183 ; 9 3 & # 183 ; 46 3 & # 183 ; 53

1 & # 183 ; 0 3 & # 183 ; 72 3 & # 183 ; 96

The above two tabular arraies are to two denary topographic points so that the information is easier to pull a graph from. I did non include the period or the period squared on my graphs because the consequences are excessively close together but the tabular arraies indicate how close my consequences were to what they should be in theory.

From my consequences I have found out that the period squared is as predicted straight relative to the length of the pendulum because my graph is a consecutive line and goes through 0. Besides if you take the length at 0 & # 183 ; 1m the period squared is 0 & # 183 ; 37 and so if you take the length at 0 & # 183 ; 5m the period squared is 1 & # 183 ; 96m. The point of this is to demo that that both the period and the length go up by about precisely the same proportion because 0 & # 183 ; 5/0 & # 183 ; 1=5 and 1 & # 183 ; 96/0 & # 183 ; 37=5 & # 183 ; 3. The graph with period plotted against length besides provides the utile information that period and length have a relationship, which involves the indice 2. I have noticed the form that if you divide the period squared of the pendulum by the length of the pendulum you get approximately the same figure each clip and that the ratio between length and the period squared is approximately 1:38.

I can pull a decision from my grounds that the expression:

This is right because if you rearrange it to organize T2= 2pl this fits absolutely

g

with the graph and my consequences. If you remove the invariables from the expression you are left with a direct nexus from T2 to l. The curve besides reinforces the original expression by demoing that as cubic decimeter additions by 0 & # 183 ; 1 the period additions by a much larger per centum. As the length increases the period goes up in smaller and smaller sums, which once more agrees with the expression. These consequences wholly back up my original anticipation and they besides support the scientific theory. The form of the graph instantly shows this. The consequences obtained show that my experiment was successful for look intoing how length effects the period of an oscillation because they are the same and agree with what I predicted would go on. The process used was non excessively bad because my consequences are really similar to what they would be under perfect fortunes. My consequences are moderately accurate as they fulfil what I thought and said would go on. However there are a few minor anomalousnesss which can be seen in the graphs and in the tabular arraies. They have a larger spread from what they should hold been harmonizing to the expression than usual. At 1m there is an anomalousness which is a few fractions of a 2nd off from the line of best tantrum.

Most of the process was suited because it gave a utile and relevant result but it could hold been improved in a figure of ways. The dependability of the grounds could be increased by doing the angle more precise, doing certain the twine is tight when the pendulum is released and doing the threading the exact length it should to be. The anomalous consequences I have may be down to a figure of grounds but could chiefly be blamed on my let go ofing the pendulum and supplying it with an external force, which would impact the period. My timing of the fillet and starting of the stop watch could be inaccurate. The overall consequences may be a 1/100 of a 2nd out because I used the gravitative field strength of 10 when the existent field strength may be different. If the above betterments were added in, the consequences would be more accurate and dependable. To further this work, I would reiterate each length supplying more accurate norms. I would supply extra grounds for my decision by increasing the scope of lengths and diminishing the intervals between the lengths to five centimeters. These add-ons would widen my probe farther.