1
Name:__________________________
PhET Exploration: Simple Harmonic Motion (SHM)
Introduction
Consider the diagram of a ma
le in a spherical bowl.
Label the ma
le's equili
ium position.
What would you expect to happen if you were to push the ma
le away from equili
ium?
Why do you think the ma
le behaves this way? (Hint: add a FBD to each ma
le!)
Can you think of another situation where you observed this kind of motion?
In your group, discuss the following terms and record your present understanding of each.
Equili
ium position
Oscillation Restoring force
2
Making Connections
An understanding of simple harmonic motion will build on concepts you have studied: period and frequency,
velocity and acceleration, springs and restoring forces, energy transformations and the conservation of energy.
Systems that Oscillate with SHM
Part I Period and Frequency
Procedure
Open a web
owser and go to the “Masses and Springs” experiment on the Phet website.
https:
phet.colorado.edu/en/simulation/masses-and-springs
When you run the simulation, you will see a selection window as below. Click on “Intro”.
The following default simulation page will appear:
There are sliding controls for the spring constants of each spring, next to each spring. They are
set to 4th increment by default. Do not change this setting for Parts A and B of the experiments.
Your slider should look like the picture below:
https:
phet.colorado.edu/en/simulation/masses-and-springs
3
We will only use Spring 1 for all parts of this experiment.
On the right side of the screen, you will see the ruler and stop-watch as seen below:
Drag and place them on the simulation screen as below to make them usable in our experiments:
Then, go to the controls on the right side and make sure “Equili
ium Position” and “Movable
Line” options are selected. Note that damping (friction) is zero by default and will stay that way
throughout this experiment. Also note that gravity can be changed by selecting one of the options
in the select menu. It is set to “Earth” by default and do not change it for Part A.
4
On the bottom right corner of the screen, mark your simulation speed to “Slow”:
Now, it is time to get the 50 gr mass and hang it on Spring 1. Drag and place it on the hook at the
tip of the spring. As soon as you do that, you will see the green line which co
esponds to the
Equili
ium position of this spring-mass system and the mass will oscillate.
If you place the hook of the spring exactly coincident with the equili
ium line (green line),
oscillation will stop. As you know, it is the equili
ium position and the net force is zero. Hold
and place the mass such that the hook is exactly coincident with the green line as seen below and
make sure there is no oscillation.
5
Now, place the ruler and the movable red line such that 10 cm is aligned with the green
(equili
ium) line and 20 cm is aligned with the movable (red) line as below:
In the first run, we will stretch the spring and mass system by 10 cm down from its equili
ium
position. This is why we placed the red line 10 cm away from the green line (indicates the stretch
position).
Before starting the oscillation, pause the simulation by clicking the right bottom corner control
(make sure slow speed is still selected):
XXXXXXXXXXsimulation is active XXXXXXXXXXsimulation is paused)
6
Activate the stop-watch by resetting and then pushing the start button on the stop watch. Note
that it won’t start until the simulation is started but it will be ready to go.
While the stop watch is active and the simulation is paused, drag your mass to the stretch
position such that hook is aligned with the red line. For the first case of 10 cm stretch, the
placing should look like below:
As soon as you hit the play simulation button (right bottom corner), the mass-spring system will
oscillate vertically around the equili
ium point and between 0 cm and 20 cm on your ruler
(oscillation amplitude is 10 cm). It will start from the bottom (20 cm) and it will go back up to 0
cm, then reverse direction to come back to the starting point (20 cm). Every time the mass comes
7
ack to 20 cm (on the ruler) it will be a complete cycle. For our experiments we will record the
time needed for ten complete cycles.
The stop- watch will start automatically when you hit “play” the simulation and you will count
the number of cycles. You will manually press “pause” on the stop-watch when the mass comes
ack to the original position the 10th time (total of 10 cycles).
Please remember that Period (T) is the time for one complete cycle of movement. In this case, you will be
ecording the time for 10 cycles, so you will find the period by dividing the total time by ten.
Part A:
Use the procedure outlined above and run experiments with 50 gram, 100 gram and 250 gram
masses and stretches of 10 cm and 20 cm to fill the tables below. Make sure to record the time
needed for 10 total cycles in each case and then calculate the period for each run.
Hint: The procedure above was described considering a stretch of 10 cm. When you are running
with stretches of 20 cm, placing the 20 cm-line on the ruler to coincide with the equili
ium
(green) line and placing the red (movable) line coincident with 40-cm mark of the ruler will be
helpful. Do not forget to reset your stop-watches before starting each separate run.
Fill in the chart below to determine the period of motion for each of the masses on Earth.
Throughout the whole experiment use 4 significant figures.
M (kg) y (m)
(stretch)
Time for 10 cycles (s) Period (s)
time/cycle
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
M (kg) y (m)
(stretch)
Time for 10 cycles (s) Period (s)
time/cycle
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
8
Part B:
Repeat the experiment on Jupiter, stretching the spring 10 cm. From the select-down menu on
the right side controls for gravity, select Jupiter instead of the Earth and repeat the procedure
for 50 gr and 100 gr masses and for 10-cm stretch. Record the total time for 10 cycles in each
un and calculated period on the table below.
Part C:
In this part, we will change the spring constant and observe its effects on oscillations. First of all, move
the gravity setting back to “Earth”. In the first two parts, we used a spring constant setting with the
slider being at the 4th mark. Now we will repeat some of the simulations with the slider set at the 7th and
10th marks as seen below:
Use a 100 gram mass and a stretch of 10 cm and run the same procedure with the two new spring
constant setting (slider at 7 and slider at 10). Fill the table below with your results
Mass (kg) Time for 10 cycles (s) Period (s) time/cycle
0.050
0.100
Spring Constant
slider position
Time for 10 cycles (s) Period (s)
time/cycle
7
10
9
Data Analysis:
1. As mass on a spring increases, the period of motion (one full up and down) increases / decreases /
emains the same.
2. As the gravitational pull (Jupiter) on a spring increases, the period of motion increases / decreases /
emains the same.
3. As the spring constant increases, the period of motion increases / decreases / remains the same.
4. Amplitude is the displacement (meters) from the equili
ium position. Does the amplitude of a spring's
movement depend upon period? Yes / No
5. What effect does a planet's gravitational field g have on the period of motion? Is it affecting the period?
Explain why.
Part D:
An equivalent piece of information is the inverse of the period, or number of cycles completed in one
second. This is the frequency f of the oscillation. The units of frequency are hertz, a
eviated Hz. By
definition,
1 Hz = 1 cycle per second = 1 s-1
Calculate the frequency for each period from parts A, B, and C.
Note: For each mass, use the average period of both stretching (10 cm and 20 cm) for Part A.
For example, for 50 gram, you should have a period for 10 cm and another one for 20 cm stretch.
Find and use the average of these two in your calculations for frequency below. From Parts B,
there are only one period determined for each mass. Use that value. From Part C, use two
different periods found for different spring constants.
From Part A
Mass (kg)
T(s) f (Hz) Sample Work:
0.050
0.100
0.250
From Part B
Mass (kg)
T(s)
0.050
0.100
From Part C
Spring Constant
Mark
T(s)
7
10
10
Part E
Applying Energy Principles
The transformations between kinetic and potential energy are important to understanding simple harmonic motion.
The diagram below shows the position of a mass on a spring at successive points in time. Label the associated free-
ody diagrams and complete the table as required.
1. There is no thermal energy change associated with the system, so conservation of energy can be written as:
Etotal = Us + K
2. Because total energy does not change, the maximum kinetic energy