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Measuring the Period of a Pendulum Motion

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Measuring the Period of a Pendulum Motion

Introduction

The purpose of the pendulum lab was to form a hypothesis by choosing if either the period of a pendulum depends more on its mass or its length, and state that my hypothesis is either right or wrong by conducting tests with different lengths and two different masses. My hypothesis states that the period of the pendulum will depend more on its length than its mass. My reasoning is that the a long string will require more time for the mass to swing from one extreme and back again than a small amount of string. When there is a longer string attached to the rod, it will take a longer amount of time to reach its full extension and back.  

Procedure

The key materials used in this lab include:

  • Meter Stick
  • Rods and Clamps
  • Wood Ball
  • Aluminum Ball
  • String
  • Scale
  • Stop Watch

First, I made my hypothesis that the length of string would affect the period of a pendulum more than its mass. We than gathered the needed materials listed above. Set-up the clamp on the table which was attached to a rod that was perpendicular to the table. Another clamp was attached at the end of that rod to hold it in place. Next, the wooden ball was measured to be .059 kg and the aluminum ball at .242 kg. The wooden ball was hung from the rod and its measured distance was .888 m. The aluminum ball was then position beside the wooden ball on the same rod and measured at the same distance from the floor; therefore, they would be positioned exactly beside each other. The wood ball was lifted to an approximated 20 degree angle with the rod (note: we maintained the same angle by placed a meter stick along the edge of the table top so when you pulled the string to the approximated angle it would touch the meter stick). I used the stop watch to time the ball when it first began to swing to when it came back and either touched or almost touched the meter stick. For the first trial it took the wood ball 1.78 seconds to complete its period. This process was repeated 10 times at the height of .888m for both the wood ball and the aluminum ball. Moreover, the wood ball had an average time of 1.79 seconds, and a standard deviation time of  0.050 seconds. The aluminum ball had an average time of 1.76 seconds, and a standard deviation time of  0.047 seconds. For the second part of the lab I had to remove the wood ball from the rod. I than moved the aluminum ball to a height of .841 m. By the same process in part 1, I moved the aluminum ball to an approximated 20 degree angle and let it commence in a pendulum motion. At the height of .841 m it took the ball 1.70 seconds to go through a full period. This was 1 of 10 different trials at the height of .841 m; its average time was 1.72 seconds with a standard deviation of 0.035. The process explained above was repeated at four more heights. The heights include 0.841m, 0.783m, 0.727m, 0.648m, and 0.558 m. Finally, all of the data including the mass of the balls was transferred to Microsoft Excel.

Data

Sphere

Mass (kg)

Wood

0.0059

Aluminum

0.0242

Trial

Wood

Metal

Length (m)

1

1.78

1.70

0.888

2

1.82

1.77

3

1.86

1.70

4

1.83

1.76

5

1.72

1.77

6

1.71

1.80

7

1.81

1.72

8

1.82

1.84

9

1.81

1.74

10

1.75

1.81

Average

1.79

1.76

Stdev

0.050

0.047

Length (m)

0.841

0.783

0.727

0.648

0.558

1

1.70

1.66

1.55

1.55

1.41

2

1.73

1.63

1.53

1.53

1.42

3

1.78

1.69

1.46

1.45

1.40

4

1.76

1.68

1.61

1.44

1.40

5

1.73

1.64

1.59

1.55

1.38

6

1.68

1.70

1.55

1.55

1.45

7

1.72

1.65

1.56

1.49

1.40

8

1.71

1.62

1.65

1.50

1.50

9

1.67

1.70

1.54

1.46

1.35

10

1.69

1.60

1.65

1.45

1.44

Average

1.72

1.66

1.57

1.50

1.42

Stdev

0.035

0.035

0.058

0.045

0.041

Sample Calculation

Average time (1) = (1.78)+(1.82)+(1.86)+(1.83)+(1.72)+(1.71)+(1.81)+(1.82)+(1.81)+(1.75)/10

                    =1.79

Average time (2) = (1.70)+(1.73)+(1.78)+(1.76)+(1.73)+(1.68)+(1.72)+(1.71)+(1.67)+(1.69)/10

                    = 1.72

Results

My hypothesis was correct; according to the data table, the period of the pendulum depends mainly on the length of the string than on its mass. For example, in the second table the wood ball and the aluminum ball took nearly the same time to complete one period at the same height. The average time for the wood ball was 1.79 seconds, and the average time for the aluminum ball was 1.76 seconds. When I changed the length of string attached to the aluminum ball, the times varied because it was located at a different height. For example, when the length of the string was 0.841 meters its average time was 1.72 seconds. When the length of the string was 0.558 meters the average time was 1.42 seconds. As the length of the string decrease, the time it took to complete one full period decreased. Therefore, the length of string to form a pendulum motion matters more than its mass for completing a period. Major sources of error in this lab could have been from not beginning or stopping the stop watch at the correct time or not measuring the length of string accurately for a certain trial. If I began the stop watch too early, the time it took the pendulum to swing one full period would have been longer than in the data table charts. If I began the stop watch too late, the time it took the pendulum to swing one full period would have been shorter. Therefore, the average time would have been altered and if the average time was altered enough in the second data table it could make my hypothesis incorrect. For example, if my average time in each trial with the wood ball was much greater than the average time for the aluminum ball, then the pendulum would depend more on its mass than its length. If the length of the string was measured inaccurately it could change the average time as well. For example, in the third table, if the actual length for the first few trials were .860m instead of .841m the time would have been greater. Moreover, the difference between the first ten trials would be even greater from the next ten trials at the length of 0.783.

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