To investigate the factors that affect the period of a pendulum

To support my theory that length has a positive correlation to period

S=d/t

T=d/s

PE=mgh mgh=1/2 mv

PE=KE gh=1/2 v

1/2 v = gh

v=2gh

v=V2gh

v Vh

The above formula shows that the relationship between the period and the length is not always directly proportional because, if you double the period it does not necessarily mean that the length of the string would have to be doubled and if you double the length then the period will not be doubled.

Galileo connects the period (t) with the length(l) as

Period = L must be converted to m

(Background info on Galileo's discovery)

Until Galileo, most scientists believed that scientific problems could be solved using deductive reasoning. They needed no testing to be believed. Galileo was one of the first to challenge this way of thinking. The Greeks thought that if an object was heavy it would fall faster than an object that was lighter. Gravity was believed to pull more strongly on heavier objects. Galileo tested this belief in his famous experiment of dropping objects of similar shape but unequal weight from a tall building. He found that distance is a function of time, and came up with this equation:

Basic Law of Falling Bodies

d=t2

(distance equals time squared)

d = t2

time 1/4 sec.

0

2

3

4

5

...

distance ft.

0

4

9

6

25

...

Galileo came to the conclusion that Aristotelian physics was in fact wrong about the relationship between speed of fall and weight. He proved that gravity is a force that acts equally on all bodies, and that the netforce on a body will not always equal zero.

GALILEO'S PARADOX

Galileo's paradox states that there are as many square numbers as integers, or as many integers as there is square numbers.

Since each number has its own square , for every integer there is a certain square number.

Galileo's Paradox

Integer

2

3

4

5

...

|

|

|

|

|

Square #

4

9

6

25

...

PENDULUMS

Galileo first became interested in pendulums at the age of 19 when he was at a church and observed a swinging chandelier. He timed the length of the pendulum's swing, or oscillation, using his pulse and made a very interesting discovery. No matter how far the chandelier swung, the length of time it took for one oscillation was always the same.

After more experiments, Galileo found that the distance and the weight of a pendulum does not make a difference in the time required for one oscillation. The length of the string is what determines time for one oscillation. This led him to discover a relationship between oscillation time and length of the pendulum:

Pendulums: Oscillation Time and String Length

Time of Oscillation

Length of Pendulum

sec.

unit

2

4

3

9

4

6

5

25

...

...

The pendulum was great as a way to measure time. The pendulum clock invented in 1660 using Galileo's discoveries was a great improvement over sand and water clocks

As a rough guess the shape of the graph I will expect will be

to get accurate results I will take 10 sets of results trying each measurement five times and use an average to plot one graph and have another graph that has all of the results

Method

I will use a range of ten lengths of string and repeat them five times.

600mm 700mm 800mm 900mm 1000mm 1100mm 1200mm 1300mm 1400mm 1600mm

by monitoring and recording the time of ten periods(at one time) and dividing that number by ten I will get the result for one period. This method is more accurate than relying on reflexes, I will then take an average of the five results and make an average and plot a graph and also plot a graph of all the results.

I may be able to use a strobe light so I will be able to see exactly where and when the pendulum finishes a period therefore making the experiment more accurate. I could also use a light gate but the pendulum would not always swing in a straight line because the earth moves and the pendulum is moving as the earth moves and so would hit the light gate . The air resistance will have no or very minute effect on my results because of the x10 approach of obtaining information.

Kit list

2 G clamps (to clamp stand to the table)

Boss clamp

Pincher clamp

Wood with screws

Stopwatch

Measuring tape

Calculator

Screwdriver

length

2

3

4

5

average

60

5.45

.55

5.51

.55

5.49

.55

5.54

.55

5.47

.55

5.492

.55

70

6.78

.68

6.83

.68

6.77

.68

6.75

.68

6.84

.68

6.79

.68

80

7.98

.80

7.96

.80

7.99

.80

8.04

.80

7.95

.80

7.984

.80

90

9.02

.90

9.04

9.0

9.00

.90

9.03

.90

9.01

.90

9.02

.90

00

20.08

2.01

20.05

2.01

20.09

2.01

20.07

2.01

20.09

2.01

20.076

2.01

10

21.06

2.11

21.08

2.11

21.12

2.11

21.09

2.11

21.13

2.11

21.096

2.11

20

21.95

2.20

21.99

2.20

21.96

2.20

21.98

2.20

21.95

2.20

21.966

2.20

30

22.85

2.29

22.89

2.29

22.88

2.29

22.86

2.29

22.88

2.29

22.872

2.29

40

23.87

2.39

23.85

2.39

23.89

2.39

23.86

2.39

23.93

2.39

23.88

2.39

60

25.35

2.54

25.42

2.54

25.43

2.54

25.38

2.54

25.44

2.54

25.404

2.54

Results

As you can see from my results all of the results are very close together in each length so it would be illogical to plot a graph that had every result on it as each result would be on the same line and I do not have a sheet of graph paper that has as many squares that would be needed to plot such a graph. So I will only plot an averages graph.

To see if my data is good I will use Galileo's formula on each of the lengths.

60cm=1.554685

70cm=1.6792516

80cm=1.7951953

90cm=1.9040923

00cm=2.0070894

10cm=2.1050537

20cm=2.1986568

30cm=2.2884341

40cm=2.378204

60cm=2.5387901

I am delighted and surprised that my results have come out so well, each set is almost in line with what Galileo's formula states that it should be. There are no anomalies that I can see so my results can lead me to a conclusion that the length of a piece of string on a pendulum affects the period in a strong positive correlation of the longer the string the longer the period I have proven Galileo's theory to be correct and there are only a few ways on how to improve this experiment; use a strobe in such a manner that you can get the bob to seemingly freeze because of either a high frequency or low frequency flashing strobe then all you would need to do is see how fast the light is flashing an there you have the period, also a light gate could be used but because of the earths revolutions the bob would hit the light gate. My graph shows a strong positive correlation between the length of string and the period of the pendulum.