Exploration of the simple pendulum

Title: An exploration of the simple pendulum

Purpose

The purpose of the experiment was to discover something about the motion of simple pendulums and to find that most and least important things that determine the period of pendulum. The difference of length would change the period of pendulum.

Apparatus and method

Meter Stick was used to measure the distance the wooden sphere that was pulled back from equilibrium at the beginning of each trial. Lab stand was used to hang the string that attaches the wooden sphere that was used to attach two different masses of the sphere (large, small) and three different lengths of the string (100cm, 75cm, and 50cm). Moreover, pendulum was set which was made of a string of length L attached to a wooden sphere and hung from a lab stand using a thumb screw. Computer was used to connect motion sensor and to see the amplitude of the pendulum which was taken from the motion sensor. Motion Sensor was used to capture the motion of the pendulum and to send the information to the computer. DataStudio was the software program used to plot the distance traveled by the wooden sphere from its starting point.

Data

Data for Part 1A

L=100cm

D=10cm

M=Large Mass

Cycle

1

2

3

4

5

6

7

8

9

10

Period

1.9969

1.9969

2.1505

2.0481

1.792

2.2529

2.1505

1.8433

2.1505

1.9456

Average Period

2.03272

Range

0.4609

StDev

±0.1469

Data for Part 1B

L=100cm

D = 10 cm

No. of Cycles (n)

Time for n cycles (in s)

Period (Time/n)

Run #1

10

20.3272

2.03272

Run #2

10

20.2248

2.02248

Run #3

10

20.3272

2.03272

Average Period

2.029306667

Range

0.01024

% Dif A&B

0.168060607

Data for Part 1C

No of Cycles (n)

Period

Length (in cm)

Run #1

10

2.03272

10

Run #2

10

2.03272

5

Run #3

10

2.03783

15

Average Period

2.034423333

Part 2

Period (in s)

Small Sphere

1.99

Large Sphere

2.03

Average Period

2.01

Part 3

Period (in s)

L = 100cm

Run #1

1.98152

100

Run #2

1.99176

Run #3

1.9952

Average Period

1.989493333

Period (in s)

L = 75

Run #1

1.74599

75

Run #2

1.75111

Run #3

1.74599

Average Period

1.747696667

Period (in s)

L = 50

Run #1

1.42342

50

Run #2

1.42342

Run #3

1.43366

Average Period

1.426833333

Calculations and Graphs

The Calculation is attached to the next page.

Results

The overall results were that when if the weight of the wooden sphere changed, the periods were almost same (average period was 2.032 with large sphere for first time and average period was 2.029 with large sphere); however, when we changed length of the string, which was attached to the wooden sphere, the periods were changed much. The longer length had more time of period (average period was 1.989 for length 100 with small sphere), and shorter length had less time of period (average period was 1.427 for length 50 with small sphere). The standard deviation was ±0.1469 when we measured with 100 cm length of the string at the first time, and percentage between part 1 and part 2 (with same length of string and mass of the sphere) was 0.168060607. Therefore, there was no analysis needed in this section.

Conclusion and Discussion

The results were well enough to prove the hypothesis that mentioned in purpose section.

However, all the data was not exactly same as the theoretical value because it was human's work. The weight of a pendulum does not affect much on the period of the pendulum

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