Analyzing A Pendulum

The purpose of this lab is to find the relationship between the time it takes the pendulum to take three entire oscillations and the length of the pendulum. We want to find the approximate time it would take the pendulum to complete three oscillations with three different lengths (1.02 m, 0.77 m & 0.53 m). Also, we want to see if the time period of oscillations becomes longer or shorter when the length of the string increases.

Hypothesis:

As the length of the string increases, the time it will take for the pendulum to complete three oscillations will increase. When the string is longer, the pendulum will have to travel a greater distance to complete an oscillation and therefore the time period will increase.

Materials:

• 1 pendulum ball

• String (1 m)

• Stopwatch

• Metre stick/ ruler

• Tape

Procedure:

1. Attach the string to the pendulum ball and using the metre stick or ruler, measure and then cut the string to one metre.

2. Tape the pendulum up so that it is suspended in the air with room for horizontal movement.

3. Make a parallel mark 40 cm from the end of the pendulum.

4. Pull the pendulum to the 40 cm mark and release. Start the stopwatch at the release, and at the end of the third oscillation, stop the timer. Record the time.

5. Repeat Step 4 three times.

6. Repeat Steps 3 - 5 with, adjusting the string lengths to 0.75 m and 0.5 m accordingly.

Observations:

Trial Length of Pendulum (m) Experimental results

Time of 3 Cycles (s) Time of 1 Cycle (s) Average

1 1.02 5.96 1.99

2 1.02 5.91 1.97

3 1.02 5.92 1.97

4 0.78 5.09 1.70

5 0.78 5.02 1.67

6 0.78 4.98 1.66

7 0.53 4.19 1.40

8 0.53 4.37 1.46

9 0.53 4.17 1.39

Analyze and Conclude Pg. 21

1) How many oscillations did you use to determine the period of the pendulum?

We used three oscillations to determine the period of the pendulum.

2) How many trials did you run before changing variables? Was this enough? Explain.

Before the actual recording of the length of the time periods, practice trials were done to ensure that timing was done correctly. In addition, two timers were used at the same time and the average of the two was recorded as the length of the period to improve accuracy. We ran three trials before changing the variable.

Running three trials was sufficient enough to show us the impact on the time period when the length is changed. It showed us that as the length of the pendulum increases, the time it would take for the pendulum to make three oscillations also increases. However, running only three trials could not give us an exact result. The results we got from the three different samples were always different from each other, only allowing us to calculate an average time it would for the pendulum to swing three oscillations.

3) Did your hypothesis include length as a variable? If so, why? If not why not? Explain your choice of variables.

Our hypothesis included length as a variable. We made an assumption that there might be a relationship between the length and the time period. We believe that the longer the length of the pendulum, the greater the distance the arm would have to travel to complete an oscillation. Therefore, because of an increase in length the time period will increase as well.

4)

Trials

Time of Cycle

1-3

1.01 %

4-6

2.38 %

7-9

4.94 %

5) According to your results, what variables affect the period of oscillation of a pendulum? Explain, providing as much detail as possible.

The length of the pendulum affected the length of each period. As the length of the string increased, the time it took for the pendulum to complete one full oscillation also increased, and vice versa. Since the distance needed to travel in order to complete one oscillation is greater with a longer pendulum, it takes a longer period of time to travel, verifying our hypothesis.

Percent of Error:

Trial Relative Uncertainty

Time 1 cycle

1

0.251 %

2

0.251 %

3

0.251 %

4

0.003 %

5

0.299 %

6

0.301 %

7

0.357 %

8

0.342 %

9

0.360 %

P. 22 -INVESTIGATION 1-BвЂ"Analyzing Pendulum Data

Purpose:

The purpose of the investigation is to see if there is error within our experimental data, and to compare out results with the theoretical value in order to determine how accurate we are.

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