This document describes an interactive simulation for investigating the factors that affect the frequency and period of a vibrating mass on a spring. It instructs users to systematically vary different factors like mass and spring stiffness while measuring the period of oscillations. The challenge is to determine what factors influence frequency and period, and describe the effects. For example, as mass increases, period increases and frequency decreases. As spring stiffness increases, period and frequency are also affected.

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Mass on a Spring Interactive
Purpose:
To determine what factors affect the frequency and the period of a vibrating mass on a spring
and to state the relationship between those variables and the frequency or period.
Getting Ready:
Navigate to the Vibrating Mass on a Spring Interactive at The Physics Classroom website:
http://www.physicsclassroom.com/Physics--‐Interactives/Waves--‐and--‐Sound/Mass--‐on--‐a--‐Spring
Navigational Path:
www.physicsclassroom.com==>Physics Interactives ==> Waves and Sound ==> Vibrating Mass on a Spring
Getting Acquainted:
Once you've launched the Interactive and resized it, experiment with the interface. Place a
mass on the end of the spring and observe the vibration. Click/tap the Start button to view the
plot of its vertical position as a function of time. Reset the system and place a mass on each
spring and observe that their graphs are color coded -‐‐consistent with the color of the spring.
Notice that the time, height, and velocity of the mass are reported below the graphs. And most
importantly for this lab, observe how the vertical line on the graph can be moved along the axis
in order to obtain values of height and velocity at various times on the graph.
The Challenge:
Your challenge is to determine what factors affect the frequency and the period of a vibrating
mass on a spring. Make your study of this question very systematic -‐‐varying one factor at a
time while you hold others constant. You can easily test the mass and the stiffness of the spring
as possible factors. If you are "quick," you might also be able to test damping as a possible
factor. Conduct several trials for each variable under study. For each trial, measure the period
by recording the difference in time from the start and the end of one cycle or of several cycles.
Use the provided tables. Not all columns or rows will necessarily be used.
Factor#1: Mass
Factor:
______Mass____
# of
Cycles
Start Time
(s)
Stop Time
(s)
Period
(s)
Frequency
(Hz)
1 kg 4 .48 2.44 0.49 2.04
2 kg 4 .16 2.96 0.7 1.428
3 kg 4 .22 3.68 0.865 1.156
4 kg 4 0.18 4.14 0.99 1.010

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Factor#2: Stiffness of the spring
Factor:
Stiffness
# of
Cycles
Start Time
(s)
Stop Time
(s)
Period
(s)
Frequency
(Hz)
1 kg 4 0.32 1.88 0.39 2.56
2 kg 4 0.38 2.61 0.56 1.79
3 kg 4 0.13 2.8 0.67 1.50
4 kg 4 0.15 3.28 0.78 1.28
Factor#3: Damping
Factor:
Damping
# of
Cycles
Start Time
(s)
Stop Time
(s)
Period
(s)
Frequency
(Hz)
1 kg 4
2 kg 4
3 kg 4
4 kg 4
Conclusion:
Identify the factors that affect the frequency and the period of a vibrating mass on a spring. For
each factor having an effect, describe the effect (e.g., state something like ..."As the
increases,theperiod andthefrequency .")
*As the mass increases, the period increases and the frequency decreases.
*As the stiffness of the spring and the mass increases, the period increases and the frequency decreases.

3. From The Physics Classroom's Physics Interactives http://www.physicsclassroom.com
©The Physics Classroom, All Rights Reserved This document should NOT appear on other websites.
Factor #1:

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©The Physics Classroom, All Rights Reserved This document should NOT appear on other websites.
Factor #2