Simple Harmonic Motion
and Newton’s 3rd Law
Theory
Simple Harmonic Motion is not as simple as the name makes it out to be but it is a fundamental part of
physics and is seen in one form or another in many different fields of study.
Something undergoing simple harmonic motion moves in a manner, which resembles a sinusoidal wave
having both a crest and a trough. The object will start from rest, rise to a maximum height and come to
a momentary pause before changing its direction. It will then fall through its at rest position to a
minimum position which is equal in magnitude to its maximum position and again come to a momentary
pause before changing its direction to move back to its rest position. It then repeats the process until
outside forces changes its motion or bring it to a stop.
The period of the motion can be predicted. In the case of a mass suspended from a spring, then the
predicted period can be found using the equation
period  2 m
k
where m is the mass of the object in kilograms and k is the spring constant.
Newton’s 3rd Law states that forces comes in pairs: when one object exerts a force on a second object
the second object exerts an equal force on the first object but in the opposite direction.
In this lab you will demonstrate Newton’s 3rd Law using two Force sensors.
Procedure:
Simple Harmonic Motion
Getting the data
1. □ Open the file shm from the 1401 folder
□ Suspend 0.550 kg from the spring.
□ On the side of the force sensor, press the TARE button.
□ Lift the mass about ½ inch straight up and release the mass.
□ Select Start from the Experiment ToolBar the computer will acquire data for 5 seconds and stop
automatically.
Analyzing the data
2. □ Within the Graph window use the mouse to select the sine waveform select as many sine waves as
possible.
□ The top bar of the graph window has a pull down menu labeled Fit. From this menu select Sine.
□ A box should appear within the graph window. The value labeled period is the number of interest.
Record this value as your measured period.
□ Using the measure period determine the spring constant, k, for the spring the equation
k = 4 2
m
t2
5. Repeat steps 1 and 2 for a hanging mass of 0.650 kg and 0.750.
6. Change Springs and repeat steps 2 – 5. Complete Data Table 2.
Data Sheet
Data Table 1
Mass
(kg)
measured period, t
(s)
spring constant
N/m
Average Spring
Constant
Data Table 2
Mass
(kg)
measured period, t
(s)
Average Spring
Constant
As the mass increases what happens to the period?
How does the spring constant affect the period?
spring constant
N/m
Newton’s 3rd Law
1. Open the file 3rdlaw from the 1401 folder.
2. Remove any masses that may be suspended on the force sensor and TARE the force sensor.
3. Select Start. Gently pull on the hook of the force sensor and observe the graph that is created. Vary
the amount of applied force. The graph shows the force that you are applying to the Force sensor.
Select STOP after you have an understanding of the relationship of the graph and the applied force.
4. Hang the second Force Sensor from the hook. Press the TARE button for each force sensor.
5. Select Start. Gently pull on the suspending Force sensor. Again, vary the amount of pulling force.
After obtaining 15 to 20 seconds of data, stop the data run.
The graphs display two forces acting upon one another.
From your observation of the graph describe how these two forces react with one another.
The pair of force displayed in the graph is the force each sensor has on the other. Where is another pair
of forces that occurred during this experiment?