Datalogging in Science

Pendulum

Experiment to investigate the relationship between period and length for a pendulum.

Overview
The pendulum was the controlling mechanism for the first accurate clocks. Until its properties were discovered we did not have clocks that could measure time with any precision. The period of a pendulum is the time it takes for it to complete one whole swing backwards and forwards. This experiment seeks to establish a relationship between the Period T and the Length L.

Apparatus

A Datalogger capable of fast logging.
A Motion Sensor with the range set to distance (metres).

Retort stand bosshead and clamp.

Thin string or wire for the pendulum

Pendulum ‘bob’. The best type is a metal sphere with a hook.

Meter stick.

Theory
In order that the oscillations of a pendulum closely approximate simple harmonic motion the angular deviation from the vertical must be less than 5 degrees throughout the work. A spherical bob acts like a convex mirror and disperses the ultrasound energy from the Motion Sensor. The Motion Sensor is a sonar device that emits ultrasonic pulses that echo off an object. The time taken between emitting and receiving is used to calculate distance.

Advice
The motion of the pendulum bob must at all times take place within the ultrasound cone of the Motion Sensor.
If noise appears in the recording try placing a vertical board behind the pendulum in line with the Sensor to form a fixed maximum distance for the Sensor.
The Sensor will not pick up the attenuated return pulse if the distance is too large. A distance of 40cm from bob to Sensor at rest is advised.

Procedure
1. Set up the apparatus as shown. Make sure that the pendulum can swing freely and that the top of the string is rigidly held in the “split-cork”

2. Measure the length of the pendulum and write the value down in a results table.

3. Position the Motion Sensor 40cm from the string when the bob is hanging at rest.
Note: The ‘bob should be level with the lower edge of the Sensor transducer when it is stationary.


4. Connect the Motion Sensor to the datalogger.

5. Connect the datalogger to the computer.

6. Open the Graph program and set it to record Distance in Fast mode.
(The distance will be from the pendulum bob to the Motion Sensor).

7. Set the pendulum swinging and check that it is swinging in a vertical plane and ensure that the amplitude of the oscillations is less than 10cm.

8. Only begin recording when satisfied that the oscillations are of the required standard. (If not, reposition the pendulum and try again).

9. Repeat the experiment 5 more times varying the length of the pendulum (down to a minimum of 20 cm).

10. Save the results. It is good practice to save the results after each successful run.


11. Determine the time for ten oscillations (and thereby deduce the period) for each of the data sets, using the Interval feature of the software

Results
Enter the results of each trial in a table as shown below. Then calculate the square of the Period values and enter them in the table.
Plot a graph of the "square of the period" against the length of the pendulum.

Question
What conclusions may be drawn about the relationship between the period of a simple pendulum and its length?

Extensions
1. Re-run the experiment for one of the chosen lengths but with a heavier mass. Does the mass affect the period?
2. Re-run the experiment for one of the chosen lengths but with a larger angle of swing. Does the angle affect the period?

Data Harvest users

1. Connect the sensor to the datalogger and the logger to the computer
2. Then click the Set Up icon to the right of this message.
3. When the software opens, click the Play button.