Experiment 7 – Period of oscillation pendulums of different lengths complete (in air)

Aim of experiment:

Main aim: To find out how the period of oscillation differ when the length of the pendulum varies.

Sub aim: To find out if the length of pendulum affects the period of oscillation proportionally.

Hypothesis:

Main hypothesis: As stated in my summary of research (continued), the longer the pendulum, the wider the arc of the oscillation, the longer the distance traveled by the pendulum. The period of oscillation should thus, be longer as the time taken to cover the distance will increase. If this is true, the period of oscillation for the pendulum with length of 5cm should be the shortest, while the period of oscillation for the pendulum with length of 15cm should be the longest.

Sub hypothesis: Based on the equation: T = 2pÖ(L/G), the length of the pendulum should not affect the period of oscillation proportionally.

Materials Needed:

- 1 pendulum (5cm)

- 1 pendulum (10cm)

- 1 pendulum (15cm)

- 1 stopwatch (up to milliseconds)

Experiment Set-up:

Experiment Procedure:

1. Raise the 15cm long pendulum at least 15cm from the ground.

2. Clamp it to a support.

3. Raise the weight, parallel to the ground and make sure the string is straight.

4. Release the weight and start the stopwatch simultaneously.

5. Stop the stopwatch after 5 oscillations are completed.

6. Repeat the experiment 4 times more for more accurate results.

7. Repeat steps 1-6 with the 10cm and 5cm long pendulums.

Independent Variable: Length of the pendulum.

Constant Variables:

1. Weight of pendulum.

2. Height to which pendulum is raised to before release.

Dependent Variable: Time the pendulum took to complete 5 oscillations. / Period of oscillation.

Results:

Length of pendulum/cm	Time taken for 5 oscillations/s	*Period of oscillation/s
5	2.81
	2.69
	2.98
	3.06
	2.84
Average time taken for 5 oscillations/s	2.876	0.5752
10	3.95
	3.97
	3.93
	3.95
	3.95
Average time taken for 5 oscillations/s	3.95	0.79
15	4.69
	4.69
	4.8
	4.48
	4.82
Average time taken for 5 oscillations/s	4.696	0.9392

* Calculated by dividing average time taken to complete 5 oscillations by 5.

Data Analysis:

The longest pendulum (15cm) took the longest time to complete 5 oscillations, 4.696s, resulting in the largest period of oscillation of 0.9392s. The shortest pendulum (5cm) took the shortest time to complete 5 oscillations, 2.876s, resulting in the shortest period of oscillation of 0.5752s. The 10cm long pendulum had a period of oscillation of 0.79s. Although the period of oscillations are not equivalent to the values derived from the equation (0.4486, 0.6344, 0.7769), the values still increase as the length of the pendulum increases. However, the period of oscillation of the pendulums of varying lengths do not increase proportionally. For example, the 10cm long pendulum does not have a period of oscillation that is twice as long as that of the 5cm long. Likewise, the period of oscillation of the 15cm long pendulum does not triple that of the 5cm long.

Conclusion:

The longer the pendulum, the longer the period of oscillation. Also, the length of the pendulum does not affect the period of oscillation proportionally. This conclusion is valid only with the following assumptions:

1. The pendulum was raised to the same height before release, and there was no external force acting on it.

2. Human error in starting and stopping the stopwatch is minimal.