In this experiment, students find the relationship between the period and mass of a spring for small oscillations. The period of the spring and the spring constant are measured with a Force Sensor and a Motion Sensor.

• PASPORT Interface
• Equal Length Spring Set (ME-8970)
• PASPORT Force Sensor (PS-2104)
• PASPORT Motion Sensor (PS-2103A)
• 90 cm Rod (ME-8738)
• 45 cm Rod (ME-8736)
• Large Table Clamp (ME-9472)
• Hooked Mass Set (SE-8759)
• Multi-Clamp (SE-9442)
• Metric Ruler

1. Hook a 200 g mass to the bottom loop of the spring. Record this value in kilograms in the Data Table below.
2. If necessary, adjust the height so that the mass and Motion Sensor are at least 15 cm apart. (Hint: It may be necessary to place the Motion Sensor on the floor.) Check that the Motion Sensor is directly beneath the mass and pointing upward to it.
3. Press the Start Button in DataStudio.
4. Pull down gently on the mass. Release it after it extends about 3 cm.
5. Record data for about 5 seconds. Press the Stop Button in DataStudio.
6. If necessary, press to auto scale the graph.
7. Press to select the Smart Tool. Use the Smart Tool to find at least 3 periods. Record the periods into the Data Table.
8. Deselect the Smart Tool.
9. From the Experiment menu button, select "Delete ALL Data Runs." Select the "OK" button when prompted.
10. Repeat the pervious steps with 500 g, 700 g, and 1000 g masses.
11. Important: Do not delete the last set of data.

Spring color: _________________

Data Table

Mass (kg)	Period 1 (s)	Period 2 (s)	Period 3 (s)
200
500
700
1000

Analysis Table

Mass (kg)	Period Squared (T2)

Graphing Period Squared versus Mass

1. Convert the values from the Data Table to the Analysis Table above: find the average period and square those values.
2. Enter the values into the Period Squared v Mass Table in DataStudio.
3. Use the Fit-Linear button at the top of the Period Squared v Mass graph to determine the slope. Record this value.

Finding the Spring Constant

4. In the Force v Position graph, use the Fit-Linear button to determine the slope.
5. Record the value of the slope.

1. In general, what pattern do you notice between the period squared and the mass of the spring?
2. Starting with y = mx + b, write an equation that represents the relationship between period squared and the mass of the spring.
3. Using this equation, what would be the period of a 2 kg mass for this spring?
4. Using this equation, what mass would generate a period of 2 seconds for this spring?
5. How would a stiffer spring change the period for the same mass?
6. Calculate the quantity 4²/k using the spring constant determined from the results of this lab.
7. Compare the quantity 4²/k to the value of the slope from the period squared versus mass graph. Account for any differences. Explain.