Module 7—Oscillatory Motion
The Period of a Weighted Spring
What makes some springs bob fast and others more slowly? Find out what influences the time it takes for a spring to oscillate by completing the following lab.
Lesson 1 Lab: Equation for the Period of a Weighted Spring
Problem
What is the equation for the period of a weighted spring?
The applet used in this simulation helps you explore the motion of a weighted vertical spring.
Open the Simple Harmonic Motion: Weighted Spring simulation, if necessary. You can learn more about the simulation and how to use it by reading Show Me found at the top of the simulation screen. Continue with the Procedure.
Procedure and Observations
Using the simulation, determine the period of the weighted spring by doing the following:
- Reset the applet (
).
- Turn on the data display (
).
- Press “Play,” and carefully watch the spring move through ten complete cycles. (One cycle is complete every time the weight passes the starting position on its way upward.)
- Stop the applet at the end of the tenth cycle.
Module 7: Lesson 1 Assignment
Remember to submit the answer to LAB 1 to your teacher as part of your Module 7: Lesson 1 Assignment.
LAB 1. In the Period Measurements table, record the time for ten cycles in the simulation. The time required to complete one cycle is the period of the weighted spring. Calculate the period from the data for ten cycles. Record the data under the column heading “With Default Settings.” You should save the Period Measurements table to your course folder. You will update the table in LAB 2, LAB 3, LAB 4, and LAB 5.
Now that you know this, you will systematically investigate the effects of changing the amplitude of release (x), the mass (kg), and the spring constant (k).
Using the simulation, determine if the period of the weighted spring is affected by the amplitude of release by doing the following:
- Reset the applet ().
- Turn on the data display ().
- Change the amplitude of release to the maximum value of 0.30 m (
).
- Press “Play,” and observe ten complete cycles. (One cycle is complete every time the weight passes the starting position on its way up.)
LAB 2. In the table, record the time for ten cycles from the data display. Record the data under the heading “With Modified Amplitude of Release.”
On the simulation, determine if the period of the weighted spring is affected by the mass by doing the following:
- Reset the applet ().
- Turn on the data display ().
- Change the mass of the weight to the maximum value of 2.00 kg (
).
- Press “Play,” and observe ten complete cycles. (One cycle is complete every time the weight passes the starting position on its way up.)
LAB 3. In the table, record the time for ten cycles from the data display. Record the data under the heading “With Modified Mass.”
On the simulation, determine if the period of the weighted spring is affected by the spring constant by doing the following:
- Reset the applet ().
- Turn on the data display ().
- Change the spring constant to the maximum value of 200 N/m (
).
- Press “Play,” and observe ten complete cycles.
LAB 4. In the table, record the time for ten cycles from the data display. Record the data under the heading “With Modified Spring Constant.”
Module 7: Lesson 1 Assignment
Remember to submit the answer to LAB 5 to your teacher as part of your Module 7: Lesson 1 Assignment.
LAB 5. Find the average time for the completion of one cycle for each of the previous steps of the procedure. (You do this by dividing the time for ten cycles by 10.) Place your results in the appropriate cells in the Period Measurements table. You will submit your completed table to your teacher for marks.
Module 7: Lesson 1 Assignment
Remember to submit the answers to LAB 6, LAB 7, LAB 8, and LAB 9 to your teacher as part of your Module 7: Lesson 1 Assignment.
Analysis
LAB 6. Has the period changed as a result of changing the amplitude of release? Explain.
LAB 7. Has the period changed as a result of changing the mass? Explain.
LAB 8. Has the period changed as a result of changing the spring constant? Explain.
LAB 9. Summarize your findings from LAB 6, LAB 7, and LAB 8 by listing the parameters that do affect the period of the weighted spring and the ones that do not have an effect.
Conclusion
The period of a weighted spring is the time required to complete one cycle. It is defined by the spring constant and the mass of the weight attached to the spring. Expressed as an equation, it is
| Quantity | Symbol | SI Unit |
| period (The period depends on the stiffness of the spring (spring constant) and the mass of the hanging object.) | T | s |
| mass of the weight | m | kg |
| spring constant | k | N/m |
This equation tells you that a larger mass will oscillate more slowly (large period) and a stiff spring will oscillate more quickly (small period).
Did you wonder about the 2π in the equation? Where does it come from? It looks like something involving a circle, doesn’t it? How is that related to the motion of a mass suspended from a spring?